If the tangents are drawn to the circlex2+y2=12 at the point where it meets the circle x2+y2−5x+3y−2=0 then the point of intersection of these tangents, is

Let (h, k) be the point of intersection of the tangents. Then, the chord of contact of tangents is the common chord of the circles x2+y2=12 and x2+y2−5x+3y−2=0The equation of the common chord is 5x−3y−10=0Also, the equation of the chord of contact ishx+ky−12=0Equations (i) and (ii) represent the same line. Therefore, h5=k−3=−12−10⇒h=6,k=−18/5Hence, the required point is (6,−18/5).