Question

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

• A. $\frac{3}{\sqrt{2}}$
• B. $\sqrt{\frac{3}{2}}$
• C. $\frac{\sqrt{2}}{3}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is B $\sqrt{\frac{3}{2}}$

Given equation of ellipse is
$x^2+2y^2-2=0$
$\frac{x^2}{2}+\frac{y^2}{1}=1$
Center is $(0,0).$
Equation of tangent to ellipse is
$y=mx\pm \sqrt{2m^2+1}$
Since, this is equally inclined to axes.
So, $m=\pm 1$
So, equation of tangents to given ellipse are
$y=x\pm \sqrt{3}$ and $y=-x\pm \sqrt{3}$
Now, distance of tangents from $(0,0)$ is
$d=\frac{\sqrt{3}}{\sqrt{2}}=\sqrt{\frac{3}{2}}$