Let a tangent to the Curve 9 x^2+16 y^2=144 i | vedclass

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Question

Equation of tangent at point $P (4 \cos 	heta, 3 \sin 	heta)$ is $\frac{x \cos 	heta}{4}+\frac{y \sin 	heta}{3}=1$ So A is $(4 \sec 	heta, 0)$ an

Vedclass · Accepted Answer

$7$

Vedclass · Answer

Equation of tangent at point $P (4 \cos 	heta, 3 \sin 	heta)$ is $\frac{x \cos 	heta}{4}+\frac{y \sin 	heta}{3}=1$ So A is $(4 \sec 	heta, 0)$ and point $B$ is $(0,3 \operatorname{cosec} 	heta)$

Length $A B =\sqrt{16 \sec ^2 	heta+9 \operatorname{cosec}^2 	heta}$ $=\sqrt{25+16 	an ^2 	heta+9 \cot ^2 	heta} \geq 7$

Let a tangent to the Curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $A B$ is $.........$

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