If frac{{√ 3 }}{a}x + frac{1}{b}y = 2 touches ellipse frac{{{x^2}}}{{{a^2}}} + frac{{{y^2}}}{{{b^2

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10-2. Parabola, Ellipse, Hyperbola

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If $\frac{{\sqrt 3 }}{a}x + \frac{1}{b}y = 2$ touches the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ then its, eccentric angle $\theta $ is equal to: ................ $^o$

A

$30$

B

$45$

C

$60$

D

$90$

Solution

$\frac{x \cos \theta}{a}+\frac{y \sin \theta}{b}=1$ ……..$(1)$

$\frac{\sqrt{3} \mathrm{x}}{2 \mathrm{a}}+\frac{1 \mathrm{y}}{2 \mathrm{b}}=1$ ……$(2)$

compare $( 1)$ and $( 2)$

$\theta=30^{\circ}$

Standard 11

Mathematics

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