The length of the tangent drawn from the mid-point of the line joining the origin and the point $(4,-4)$, to…
The length of the tangent drawn from the mid-point of the line joining the origin and the point $(4,-4)$, to the circle $2 x^2+2 y^2-y=0$ is units
$3 \sqrt{2}$
$\sqrt{2}$
$\sqrt{10}$
3
Solution
The mid-point of line joining origin and the point $(4,-4)$ is $P(2,-2)$, so the length of tangent drawn from point $P(2,-2)$ to the given circle $2 x^2+2 y^2-y=0$ or $x^2+y^2-\frac{y}{2}=0$ is
$
\sqrt{(2)^2+(-2)^2-\frac{(-2)}{2}}=\sqrt{4+4+1}=3 \text { units. }
$