The locus of a point which moves such that the tangents from it to the two circles x2+y2−5x−3=0 and 3x2+3y2+2x+4y−6=0 are equal, is given by

Let P (h, k) be the coordinates of a point from which equal tangents are drawn to the circles x2+y2−5x−3=0  and 3x2+3y2+2x+4y−6=0. Then,h2+k2−5h−3=h2+k2+23h+43k−2⇒ 17h+4+3=0Hence, the locus of (h, k) is 17x+4y+3=0ALITER Required locus is the radical axis of the given circles and its equation is given by S1−S2=0⇒x2+y2−5x−3−x2+y2+23x+43y−2=0⇒17x+4y+3=0