The polar of (1,-2) with respect to x2+y2-10 x-10 y+25=0 is

Question

The polar of (1,-2) with respect to x2+y2-10 x-10 y+25=0 is (A) 4 x+7 y+30=0 (B) 4 x+7 y-30=0 (C) 4 x-7 y+30=0 (D) x+y=0

Tardigrade Admin · Accepted Answer

Given circle is, x2+y2-10 x-10 y+25=0 Given point ' P is (1,-2) Equation of polar of point P with respect to circle is, x ⋅ 1+y(-2)-10((x+1/2))-10((y-2/2))+25=0 ⇒ x-2 y-5(x+1)-5(y-2)+25=0 ⇒ x-2 y-5 x-5-5 y+10+25=0 ⇒ -4 x-7 y+30=0 ⇒ 4 x+7 y-30=0

Q. The polar of $(1, - 2)$ with respect to $x^{2} + y^{2} - 10 x - 10 y + 25 = 0$ is

$4 x + 7 y + 30 = 0$

$4 x + 7 y - 30 = 0$

$4 x - 7 y + 30 = 0$

$x + y = 0$

Q. The polar of (1,−2) with respect to x2+y2−10x−10y+25=0 is

4x+7y+30=0

4x+7y−30=0

4x−7y+30=0

x+y=0

Given circle is, x2+y2−10x−10y+25=0 Given point ' P is (1,−2) Equation of polar of point P with respect to circle is, x⋅1+y(−2)−10(2x+1​)−10(2y−2​)+25=0 ⇒x−2y−5(x+1)−5(y−2)+25=0 ⇒x−2y−5x−5−5y+10+25=0 ⇒−4x−7y+30=0 ⇒4x+7y−30=0

Q. The polar of $(1, - 2)$ with respect to $x^{2} + y^{2} - 10 x - 10 y + 25 = 0$ is

$4 x + 7 y + 30 = 0$

$4 x + 7 y - 30 = 0$

$4 x - 7 y + 30 = 0$

$x + y = 0$