If any tangent to the ellipse frac{{{x^2}}}{{ | vedclass

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Question

(b) The tangent at $(a\cos 	heta ,\,b\sin 	heta )$ to the ellipse is

$\frac{{(a\cos 	heta )x}}{{{a^2}}} + \frac{{(b\sin 	heta )y}}{{{b^2}}} = 1

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(b) The tangent at $(a\cos 	heta ,\,b\sin 	heta )$ to the ellipse is

$\frac{{(a\cos 	heta )x}}{{{a^2}}} + \frac{{(b\sin 	heta )y}}{{{b^2}}} = 1$ or $\frac{x}{{(a/\cos 	heta )}} + \frac{y}{{(b/\sin 	heta )}} = 1$

$	herefore $ Intercepts are, $h = \frac{a}{{\cos 	heta }},\,\,k = \frac{b}{{\sin 	heta }}$

==> $\frac{{{a^2}}}{{{h^2}}} + \frac{{{b^2}}}{{{k^2}}} = 1$.

If any tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ cuts off intercepts of length $h$ and $k$ on the axes, then $\frac{{{a^2}}}{{{h^2}}} + \frac{{{b^2}}}{{{k^2}}} = $

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