The mid-point of a chord of the ellipse x2+4 y2-2 x+20 y=0 is (2,-4). The equation of the chord is

Question

The mid-point of a chord of the ellipse x2+4 y2-2 x+20 y=0 is (2,-4). The equation of the chord is (A) x - 6 y = 26 (B) x + 6 y = 26 (C) 6 x - y = 26 (D) 6 x + y = 26

Tardigrade Admin · Accepted Answer

Equation of chord at (2,-4) is T=S' ⇒ 2 x+4 y(-4)-(x+2)+10(y-4) =(2)2+4(-4)2+2(2)+20(-4) ⇒ 2 x-16 y-x-2+10 y-40 =4+64-4-80 ⇒ x-6 y=42-16 ⇒ 26

Q. The mid-point of a chord of the ellipse $x^{2} + 4 y^{2} - 2 x + 20 y = 0$ is $(2, - 4)$ . The equation of the chord is

x - 6 y = 26

x + 6 y = 26

6 x - y = 26

6 x + y = 26

Equation of chord at $(2, - 4)$ is
$T = S^{'}$
$\Rightarrow 2 x + 4 y (- 4) - (x + 2) + 10 (y - 4)$
$= (2)^{2} + 4 (- 4)^{2} + 2 (2) + 20 (- 4)$
$\Rightarrow 2 x - 16 y - x - 2 + 10 y - 40$
$= 4 + 64 - 4 - 80$
$\Rightarrow x - 6 y = 42 - 16$
$\Rightarrow 26$

Q. The mid-point of a chord of the ellipse x2+4y2−2x+20y=0 is (2,−4). The equation of the chord is