Tangents and Normals: Difference between revisions
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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]] | |||
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===== Construction of Tangents to an Ellipse ===== | ===== Construction of Tangents to an Ellipse ===== | ||
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| [[File:Tangent-Ellipse.png |350px]] | |||
| [[File:Tangent-PointEllipse.png |350px]] | |||
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===== Construction of Tangents to a Parabola ===== | ===== Construction of Tangents to a Parabola ===== | ||
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| [[File:Tangent-Parabola.png|250px]] | |||
| [[File:Tangent-Parabola2.png|250px]] | |||
| [[File:Tangent-Parabola3.png|250px]] | |||
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<hr /> | <hr /> | ||
[[File:ConicsProperties.png |350px|right]] | [[File:ConicsProperties.png |350px|right]] | ||
Revision as of 18:38, 7 April 2015
Tangents are lines just touching a given curve and its Normal is a line perpendicular to it at the point of contact (or point of Tangency).
Taking the common case of a 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.
Construction of Tangents to an Ellipse
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Construction of Tangents to a Parabola
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Tangents and Normals are two terms used to describe properties of all conics. Other common properties are as follows:
- A Chord is a straight line joining two points on the curve.
- A Focal Chord is a Chord which passses through the Focus
- The mid-points of parallel Chords lie in a straight line called a Diameter
- A perpendicular from a point on the Axis is called an Ordinate and if it goes straight across to the other side, it is a Double Ordinate.
- The Double Ordinate through the Focus is the Latus Rectum (translates from Latin as ‘The Right Side’).
- A Normal to any conic is at right angles to a Tangent at the Point of Contact