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The mid-point of a chord of the ellipse $x^2+4 y^2-2 x+20 y=0 \quad$ is $(2,-4)$. The equation of the chord is
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Verified Answer
The correct answer is:
$x-6 y=26$
Equation of chord at $(2,-4)$ is
$$
\begin{aligned}
& T=S^{\prime} \\
& \Rightarrow \quad 2 x+4 y(-4)-(x+2)+10(y-4) \\
& =(2)^2+4(-4)^2+2(2)+20(-4) \\
& \Rightarrow \quad 2 x-16 y-x-2+10 y-40 \\
& =4+64-4-80 \\
& \Rightarrow \quad x-6 y=42-16 \Rightarrow 26 \\
&
\end{aligned}
$$
$$
\begin{aligned}
& T=S^{\prime} \\
& \Rightarrow \quad 2 x+4 y(-4)-(x+2)+10(y-4) \\
& =(2)^2+4(-4)^2+2(2)+20(-4) \\
& \Rightarrow \quad 2 x-16 y-x-2+10 y-40 \\
& =4+64-4-80 \\
& \Rightarrow \quad x-6 y=42-16 \Rightarrow 26 \\
&
\end{aligned}
$$
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