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  4. 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

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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

EAMCETEAMCET 2013

Solution:

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