The value of lambda , for which the line 2x - | vedclass

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Question

(d) We know that the equation of the normal at point $(a\cos 	heta ,\,b\sin 	heta )$ on the curve ${x^2} + \frac{{{y^2}}}{4} = 1$ is given by

$ax

Vedclass · Accepted Answer

$\frac{3}{8}$

Vedclass · Answer

(d) We know that the equation of the normal at point $(a\cos 	heta ,\,b\sin 	heta )$ on the curve ${x^2} + \frac{{{y^2}}}{4} = 1$ is given by

$ax\sin 	heta - by{m{cosec }}	heta = {a^2} - {b^2}$.....$(i)$

Comparing equation $(i)$ with $2x - \frac{8}{3}\lambda y = - 3$. We get,

$a\sin 	heta = 2$, $b{m{ cosec}}	heta = \frac{8}{3}\lambda $ or $ab = \frac{{16}}{3}\lambda $.....$(ii)$

$\because \,a = 1,\,b = 2$; $2 = \frac{{16}}{3}\lambda $ or $\lambda = 3/8$

The value of $\lambda $, for which the line $2x - \frac{8}{3}\lambda y = - 3$ is a normal to the conic ${x^2} + \frac{{{y^2}}}{4} = 1$ is

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