The pole of the straight line $9x+y-28=0$ with respect to the circle $2x^2+2y^2-3x+5y-7=0,$ is

detailed solution

Correct option is C

Let (h, k) be the pole of the line 9x+y−28=0 with respect to the circle x2+y2−32x+52y−72=0 Then, the equation of the polar is hx+ky−34(x+h)+54(y+k)−72=0⇒ xh−34+yk+54−34h+54k−72=0⇒ x(4h−3)+y(4k+5)−3h+5k−14=0This equation and 9x+y-28=0 represent the same line. ∴    4h−39=4k+51=−3h+5k−14−28=λ (say) ⇒    h=3+9λ4,k=λ−54,−3h+5k−14=−28λ⇒    −33+9λ4+5λ−54−14=−28λ⇒ −9−27λ+5λ−25−56=−112λ⇒ −22λ−90=−112λ⇒ 90λ=90⇒λ=1Hence, the pole of the given line is (3, -1).