Tangents drawn from the point (a$$,$$2) to the hyperbola $$x216$$−$$y29=1$$ are perpendicular then the value of $$a2is$$

Hyperbola in conic sections

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Question

$Tangents drawn from the point (a, 2) to the hyperbola \frac{x^{2}}{16} - \frac{y^{2}}{9} = 1 are perpendicular then the value of a^{2} i s$

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Solution

$Since tangents drawn from the point A (a, 2) are perpendicular,$
$A must lie on the director circle x^{2} + y^{2} = 7. Putting x = a and y = 2,$
$we get the value of a^{2} = 3$

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