Number of tangents to circle x^2 + y^2 = 3 , which are normal to ellipse 4x^2 + 9y^2 = 36 , is

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10-2. Parabola, Ellipse, Hyperbola

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Number of tangents to the circle $x^2 + y^2 = 3$ , which are normal to the ellipse $4x^2 + 9y^2 = 36$ , is

A

$0$

B

$1$

C

$2$

D

$3$

Solution

$3x\sec \theta – 2y\cos ec\theta = 5$

$\frac{5}{{\sqrt {9{{\sec }^2}\theta + 4\cos e{c^2}\theta } }} = \sqrt 3 $

But min. value of $9{\sec ^2}\theta + 4\cos e{c^2}\theta $ is $25$

$\therefore$ no tangent

Standard 11

Mathematics

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