Let point of contact be
(x1,y1). Given, equation of circle is
x2+y2−4x−6y−12=0∴ Equation of chord of contact at point
(x1,y1) is
xx1+yy1−2(x+x1)−3(y+y1)−12‌=0⇒‌‌x(x1−2)+y(y1−3)−2x1−3y1−12‌=0But it is given that point of contact is
‌3x+4y+7=0‌∴‌‌‌=‌=−‌On taking Ist and last terms,
7x1−14=−(6x1+9y1+36) ⇒‌‌13x1+9y1+22=0On taking IInd and last terms,
‌7y1−21=−(8x1+12y1+48)⇒‌‌8x1+19y1+27=0On solving Eqs. (i) and (ii), we get
x1=−1,y=−1Hence, required point of contact is
(−1,−1).