Question

$\frac{x}{a}+\frac{y}{b}=\sqrt{2}$ touches the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1at$

• A. $0^{\circ }$
• B. ${90}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

(The correct option is 'C'

Equation of ellipse,

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Given equation of tangent,

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

General equation of tangent,

$\frac{x\cos \theta }{a}+\frac{y\sin \theta }{b}=1$

Compare this to equation (1)

$\frac{x}{\sqrt{2}a}+\frac{y}{\sqrt{2}b}=1$

So;

$\cos \theta =\frac{1}{\sqrt{2}}\text{and}\sin \theta =\frac{1}{\sqrt{2}}$

$\text{Hence}\theta ={45}^{\circ }=\pi /4$