The equation of line joining the centre of circle x2+y2=81 and the point (−2,3) is y−0=‌
3−0
−2−0
(x−0) ⇒y=−‌
3
2
x ⇒‌‌3x+2y=0...(i) The equation of line perpendicular to line (i) is 2x−3y+λ=0 ∵ It is possess through (−2,3) ∴‌‌2⋅(−2)−3⋅(3)+λ=0 ⇒‌‌λ=13 ∴ Required equation of line is 2x−3y+13=0 ⇒‌‌2x−3y=−13 Alternate Required equation of line is S1=T
(−2)2+(3)2−81=−2x1+3y1−81
⇒‌‌4+9=−2x1+3y1 ⇒‌‌2x1−3y1=−13 Replace x1 and y1 by x and y respectively, 2x−3y=−13