The normal to the hyperbola x^2a^2-y^29=1 at the point (8,3√3) on it passes through the po…

Question

The normal to the hyperbola $\dfrac{x^2}{a^2}-\dfrac{y^2}9=1$ at the point $(8,3\sqrt3)$ on it passes through the point:

Accepted Answer

Given hyperbola : $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over 9} = 1$$

$$\because$$ It passes through $$(8,3\sqrt 3 )$$

$$\because$$ $${{64} \over {{a^2}}} - {{27} \over 9} = 1 \Rightarrow {a^2} = 16$$

Now, equation of normal to hyperbola

$${{16x} \over 8} + {{9y} \over {3\sqrt 3 }} = 16 + 9$$

$$ \Rightarrow 2x + \sqrt 3 y = 25$$ ...... (i)

$$\left( { - 1,9\sqrt 3 } \right)$$ satisfies (i)

Solutions · 1