Question

The distance of the center of the ellipse $x^2+2y^2-2=0$ from those tangents to the ellipse which are equally inclined to both the axes is

• A. $\sqrt{\frac{2}{3}}$
• B. $\sqrt{\frac{3}{2}}$
• C. $\frac{\sqrt{3}}{2}$
• D. None of these

Answer 1

Answer: (B)

$\sqrt{\frac{3}{2}}$

The equation of the given ellipse is $\frac{x^2}{2}+\frac{y^2}{1}=1$

Any tangent to the ellipse is $y=mx\pm \sqrt{2m^2+1}$

Since it is equally inclined to the axes, so $m=\pm 1$

Therefore, the tangents are $y=\pm x\pm \sqrt{3}$

Distance of any of these tangents from the origin is $\sqrt{\frac{3}{2}}$