Tangents and Normals - Revision history

DT Online: Added Template

2016-06-02T19:25:17Z

Added Template

← Older revision		Revision as of 19:25, 2 June 2016
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	~~===== Terminology =====~~
	[[File:CircleParts.png \|300px\|right]]		[[File:CircleParts.png \|300px\|right]]
			__TOC__


			===== Description=====

	[https://en.wikipedia.org/wiki/Tangent '''Tangents'''] are lines ''just touching'' a given curve and its [https://en.wikipedia.org/wiki/Normal_%28geometry%29 '''Normal'''] is a line perpendicular to it at the point of contact ''(or point of '''Tangency''')''.		[https://en.wikipedia.org/wiki/Tangent '''Tangents'''] are lines ''just touching'' a given curve and its [https://en.wikipedia.org/wiki/Normal_%28geometry%29 '''Normal'''] is a line perpendicular to it at the point of contact ''(or point of '''Tangency''')''.
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	Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.<div style="clear: both;"></div>		Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.<div style="clear: both;"></div>
	~~[[File:TangentPointCircle.png \|350px\|left]]~~		<hr />

	===== To construct a Tangent to a Circle from a point outside its circumference: =====		===== To construct a Tangent to a Circle from a point outside its circumference: =====

			[[File:TangentPointCircle.png \|350px\|right]]
	* Join the point to the circle centre.		* Join the point to the circle centre.
	* Draw a semi-circle on this line as the diameter.		* Draw a semi-circle on this line as the diameter.
	* The Point of Contact (''or Tangency)'' for the Tangent is where the semi-cicle intersects the circle and its Normal joins this point to the circle centre ''[[Circles\|(angle in semi-circle)]]''.		* The Point of Contact (''or Tangency)'' for the Tangent is where the semi-cicle intersects the circle and its Normal joins this point to the circle centre ''[[Circles\|(angle in semi-circle)]]''.
	<hr />		<hr />

	===== Construction of Tangents to an Ellipse =====		===== Construction of Tangents to an Ellipse =====

	'''To construct a Tangent to an Ellipse from any point on the curve:'''		'''To construct a Tangent to an Ellipse from any point on the curve:'''
	* Join the point to each of the two Foci as shown and bisect the angle found between the two lines.		* Join the point to each of the two Foci as shown and bisect the angle found between the two lines.
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	\|}		\|}
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	===== Construction of Tangents to a Parabola =====		===== Construction of Tangents to a Parabola =====

	'''Three methods to construct a Tangent to a point on the Parabola'''		'''Three methods to construct a Tangent to a point on the Parabola'''

	Method 1.		'''Method 1.'''
	* Join the point to the Focus and draw from it a perpendicular to the Directrix.		* Join the point to the Focus and draw from it a perpendicular to the Directrix.
	* The bisector of the two lines created is the Tangent and its Normal may be constructed at right angles to it.		* The bisector of the two lines created is the Tangent and its Normal may be constructed at right angles to it.
	Method 2.		'''Method 2.'''
	* Draw a line from the point perpendicular to the Axis ''(i.e. an Ordinate)''		* Draw a line from the point perpendicular to the Axis ''(i.e. an Ordinate)''
	* With the Vertex as centre and radius the distance from the Vertex to where the Ordinate intersects the Axis, draw a semi-circle.		* With the Vertex as centre and radius the distance from the Vertex to where the Ordinate intersects the Axis, draw a semi-circle.
	* Draw the Tangent to the point from where the semi-circle cuts the Axis as shown and its Normal may be constructed at right angles to it.		* Draw the Tangent to the point from where the semi-circle cuts the Axis as shown and its Normal may be constructed at right angles to it.
	Method 3.		'''Method 3.'''
	* Join the point to the Focus construct a line at right angles to it from the Focus.		* Join the point to the Focus construct a line at right angles to it from the Focus.
	* Draw the Tangent to the point from the line's intersection the Directrix and its Normal may be constructed at right angles to it.		* Draw the Tangent to the point from the line's intersection the Directrix and its Normal may be constructed at right angles to it.
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	* A line drawn perpendicular to DF will intersect the Parabola at a Point of Tangency(T).		* A line drawn perpendicular to DF will intersect the Parabola at a Point of Tangency(T).
	* Construct a perpendicular to the Tangent from its Point of Tangency(T) to create its Normal.		* Construct a perpendicular to the Tangent from its Point of Tangency(T) to create its Normal.









	<hr />		<hr />
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	===== Other terms common to all conics =====		===== Other terms common to all conics =====

	'''Tangents''' and '''Normals''' are two terms used to describe properties of all conics. Other common properties are as follows:		'''Tangents''' and '''Normals''' are two terms used to describe properties of all conics. Other common properties are as follows:

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			{{Drawing Instruments Buyers Guide}}

	[[Category:Secondary]]		[[Category:Secondary]]
	[[Category:Geometry]]		[[Category:Geometry]]

DT Online at 17:15, 13 August 2015

2015-08-13T17:15:08Z

← Older revision		Revision as of 17:15, 13 August 2015
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	Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.		Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.<div style="clear: both;"></div>
	[[File:TangentPointCircle.png \|350px\|left]]		[[File:TangentPointCircle.png \|350px\|left]]
	===== To construct a Tangent to a Circle from a point outside its circumference: =====		===== To construct a Tangent to a Circle from a point outside its circumference: =====

DT Online: Added construction of a Tangent from a point outside the Parabola

2015-04-10T07:17:04Z

Added construction of a Tangent from a point outside the Parabola

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 | [[File:Tangent-Parabola3.png|250px]]
 |}
 <hr />
 [[File:ConicsProperties.png |350px|right]]

DT Online at 17:41, 8 April 2015

2015-04-08T17:41:32Z

← Older revision		Revision as of 17:41, 8 April 2015
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			===== Terminology =====
	[[File:CircleParts.png \|300px\|right]]		[[File:CircleParts.png \|300px\|right]]

DT Online: Added heading

2015-04-08T09:12:39Z

Added heading

← Older revision		Revision as of 09:12, 8 April 2015
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	[[File:ConicsProperties.png \|350px\|right]]		[[File:ConicsProperties.png \|350px\|right]]

			===== Other terms common to all conics =====
	'''Tangents''' and '''Normals''' are two terms used to describe properties of all conics. Other common properties are as follows:		'''Tangents''' and '''Normals''' are two terms used to describe properties of all conics. Other common properties are as follows:

DT Online: /* Construction of Tangents to a Parabola */

2015-04-08T09:08:33Z

Construction of Tangents to a Parabola

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 ===== Construction of Tangents to a Parabola =====
 {|
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DT Online: Added construction of tangents to an ellipse

2015-04-08T07:23:34Z

Added construction of tangents to an ellipse

← Older revision		Revision as of 07:23, 8 April 2015
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	<hr />		<hr />
	===== Construction of Tangents to an Ellipse =====		===== Construction of Tangents to an Ellipse =====
			'''To construct a Tangent to an Ellipse from any point on the curve:'''
			* Join the point to each of the two Foci as shown and bisect the angle found between the two lines.
			* The bisector is the Normal and a Tangent may be drawn at right angles to it.
			'''To construct a Tangent to an Ellipse from any point outside the curve:'''
			* Strike an arc with the point as centre and radius equal to its distance from the Focus as shown.
			* Strike a second arc with the second Focus as centre and radius set to equal the Major Axis.
			* Join the points of intersection of the two arcs to the second Focus as shown.
			* Where the two lines intersect the curve give the two Points of Tangency.
			* Join the point to these Points of Tangency to produce the two possible Tangents and their Normals may be drawn at right angles to them.
	{\|		{\|
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DT Online: Added 'To construct a Tangent to a Circle from a point outside its circumference'

2015-04-07T22:10:12Z

Added 'To construct a Tangent to a Circle from a point outside its circumference'

← Older revision		Revision as of 22:10, 7 April 2015
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	Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.		Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.
	[[File:TangentPointCircle.png \|350px\|left]]		[[File:TangentPointCircle.png \|350px\|left]]
			===== To construct a Tangent to a Circle from a point outside its circumference: =====
			* Join the point to the circle centre.
			* Draw a semi-circle on this line as the diameter.
			* The Point of Contact (''or Tangency)'' for the Tangent is where the semi-cicle intersects the circle and its Normal joins this point to the circle centre ''[[Circles\|(angle in semi-circle)]]''.
	<hr />		<hr />
	===== Construction of Tangents to an Ellipse =====		===== Construction of Tangents to an Ellipse =====

DT Online: Added tangents to ellipse and parabola

2015-04-07T18:38:36Z

Added tangents to ellipse and parabola

← Older revision		Revision as of 18:38, 7 April 2015
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	Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.		Taking the common case of a '''[[Circles\|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.
			[[File:TangentPointCircle.png \|350px\|left]]
	<hr />		<hr />
	===== Construction of Tangents to an Ellipse =====		===== Construction of Tangents to an Ellipse =====
			{\|
			\|-
			\| [[File:Tangent-Ellipse.png \|350px]]
			\| [[File:Tangent-PointEllipse.png \|350px]]
			\|}
	<hr />		<hr />
	===== Construction of Tangents to a Parabola =====		===== Construction of Tangents to a Parabola =====
			{\|
			\|-
			\| [[File:Tangent-Parabola.png\|250px]]
			\| [[File:Tangent-Parabola2.png\|250px]]
			\| [[File:Tangent-Parabola3.png\|250px]]
			\|}
	<hr />		<hr />
	[[File:ConicsProperties.png \|350px\|right]]		[[File:ConicsProperties.png \|350px\|right]]

DT Online: Added properties of all conics

2015-04-07T17:59:39Z

Added properties of all conics

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-[[File:CircleParts.png |350px|right]]
+[[File:CircleParts.png |300px|right]]
 [https://en.wikipedia.org/wiki/Tangent '''Tangents'''] are lines ''just touching'' a given curve and its [https://en.wikipedia.org/wiki/Normal_%28geometry%29 '''Normal'''] is a line perpendicular to it at the point of contact ''(or point of '''Tangency''')''.
@@ Line 5: / Line 5: @@
 Taking the common case of a '''[[Circles|Circle]]''', the '''Normal''' to a '''Tangent''' from a point '''P''' on the circumference is a line joining the point to the circle centre - and the '''Tangent''' is at right angles to the '''Normal'''. This forms the basis for methods of constructing '''Tangents''' such that the '''Point of Tangency''' is given accurately.
 [[Category:Secondary]]
 [[Category:Geometry]]