Question

1. Find the pole of the line
i) x + y + 2 = 0 with respect to the circle x² + y2 - 4x + 6y - 12 = 0
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Answer 1

Answer:

Given equation of polar-

x+y−2=0.....(1)

Let P(h,k) be the pole of line x+y=2 w.r.t the circle x2+y2−4x+6y−12=0

Therefore the polar of  P w.r.t. the circle is-

hx+ky−2(x+h)+3(y+k)−12=0

(h−2)x+(k+3)y−2h+3k−12=0.....(2)

Now equation (1)&(2) are same.

Therefore,

1h−2=1k+3=2−2h+3k−12

⇒4h−3k+8=0.....(3)

⇒2h−k+18=0.....(4)

Multiplying equation (4) by 3, we get

6h−3k+54=0.....(5)

Subtracting equation (3) from (5), we have

(6h−3k+54)−(4h−3k+8)=0

⇒2h+46=0