First slide

Parabola

Question

$Tangents are drawn to the parabola (x - 3)^{2} + (x + 4)^{2} = \frac{(3 x - 4 y - 6)^{2}}{25} at the extremities of the chord 2 x - 3 y - 18 = 0$
$Then the angle between the tangents is$

Moderate

A

$90^{0}$
B

$45^{0}$
C

$60^{0}$
D

$30^{0}$

Solution

$The given chord 2 x - 3 y - 18 = 0 satisfies the point (3, - 4) which is the focus of the given parabola. Hence, it is a$ $focal chord and the tangents at extremities are perpendicular.$
$(\sin c e t h e \tan g e n t s d r a w n a t t h e e n d s o f a f o c a l c h o r d i n t e r s e c t s o n t h e d i r e c t r i x a n d a n g l e b e t w e e n t h e m i s \frac{π}{2})$

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