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Asked by hemanthpakkela | 24 Feb, 2024, 04:18: PM

Let (h.k) be the pole of line x+y+2 = 0 with respect to circle  x2+y2-4x+6y+2 = 0 .

Then equation of polar is

h x + ky -2(h+x)+3(k+y)+2 = 0

(h-2) x + (k+3)y +( -2h +3k+2 ) = 0

By comparing above equation with the equation of line x+y+2 = 0 , we get

h-2 = k+3 = ( -2h +3k+2 )/2

hence , we get ,  2(h-2) = ( -2h +3k+2 )   or  4h - 3 k = 6  .........................(1)

2(k+3) = ( -2h +3k+2 )  or  2h - k = -4  ...........................(2)

Pole of line x+y+2 = 0 with respect to circle  x2+y2-4x+6y+2 = 0  is ( -9, -14 )

Answered by Thiyagarajan K | 24 Feb, 2024, 09:18: PM

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