Conic Section - Hyperbola

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Information about Conic Section - Hyperbola

Published on March 10, 2014

Author: ednexa



Conic Section - Hyperbola by

Hyperbola 1. Equation of the tangent to the hyperbola (x2/a2) – (y2/b2) =1 i. at P (x1,y1) is 1 1 2 2 xx yy 1 a b   ii. at P (θ) is x y sec tan 1 a b    iii. in terms of slope m is y = mx 2 2 2 a m b  and point of contact is 2 2 a m b , . c c        2. Equation of the normal to the hyperbola (x2/a2) – (y2/b2) =1 i. at P (x1,y1) is 2 2 2 2 1 1 a x b y a b x y    ii. at P (θ) is 2 2ax by a b . sec tan      3. Equation of the director circle of the hyperbola is x2+y2=a2-b2(a>b). 4. If the tangent at P on the hyperbola meets the directrix in F, then PF subtends a right angle at the corresponding focus.

5. The tangents at the extremities of the latus rectum of the hyperbola meets on the directrix of the hyperbola. 6. The tangent at a point P on a hyperbole bisects the angle between the focal radii of the point P. 7. The product of the lengths of perpendiculars from the foci on any tangent to the hyperbola 2 2 2 2 x y 1 a b   is equal to b2. For more study material visit -Team Ednexa

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