The given equation of circles ‌S1:x2+y2+8x+2y+10=0 ‌S2:x2+y2+7x+3y+10=0 As we know the equation of radical axis of two circles is given by S1‌−S2=0 ⇒(x2+y2+8x+2y+10) ‌−(x2+y2+7x+3y+10)=0 ⇒(8x−7x)+(2y−3y)=0 ⇒x−y=0 Thus, equation of radical axis of the given circle is x−y=0 Hence, the image of the point (3,4) with respect to y=x line is (4,3).