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

Step-by-step 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- y 2 =0 is (2)^2+(-2)^2- (-2) 2 = 4+4+1 =3 units.