Question

Find the lengths of the tangents drawn to the circle $2x^2+2y^2=3$ from the point (-2, 3) .

Answer 1

For a circle $x^2+y^2+2gx+2fy+c=0$, length of tangent from an external point $(x_1,y_1)$ is given by

$L=\sqrt{{x_1}^2+{y_1}^2+2g{x}_1+2f{y}_1+c}$

For the given circle $2x^2+2y^2=3$,

$L=\sqrt{4+9+2\left(0\right)(-2)+2\left(0\right)\left(3\right)-\frac{3}{2}}$

$L=\sqrt{\frac{23}{2}}=\frac{1}{2}\sqrt{46}$