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

Options

A. `3/(sqrt2)`
B. `(sqrt3)/2`
C. `(sqrt2)/3`
D. `sqrt(3/2)`

Answer

D

Explanation

Equation of ellipse is `(x^(2))/2+(y^(2))/1=1`. General tangent to the ellipse of slope m is `y=mxpmsqrt(2m^(2)+1)`
since this is equally inclined to axes, so `m=pm1` Thus tangents are `y=pmxpmsqrt(2+1)=pmxpmsqrt3`
Distance of any tangent from origin is then equal to `sqrt(3/2)`.