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

$90^{o}$
B

$45^{o}$
C

$60^{o}$
D

$30^{o}$

Solution

$The given chord 2 x - 3 y - 18 = 0 satisfies the point$
$(3, - 4) which is the focus of the given parabola. Hence, it is a$
$focal chord and the tangents at extremities are perpendicular.$

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