Question

Two distinct chords drawn from the point $(p,q)$ on the circle $x^2+y^2=px+qy$, where $pq\ne 0$, are bisected by $x$-axis, Then

• A. $\left|p\right|=\left|q\right|$
• B. $p^2=8q^2$
• C. $p^2<8q^2$
• D. $p^2>8q^2$

Answer 1

Answer: (D)

$p^2>8q^2$

$x^2+y^2-px-qy=0$
Let $T=S_1$
$\alpha x+oy-\frac{p}{2}(x+2)-\frac{q}{2}\left(y\right)={\alpha }^2-p^2$ put $\left(x^{\prime }y\right)-(p-q)$
$p\alpha -\frac{p}{2}(p+\alpha )-\frac{q}{2}\left(q\right)={\alpha }^2-p^2$
$p\alpha -p^2-p\alpha -q^2=2{\alpha }^2-p\alpha$
$2{\alpha }^2-4p\alpha +p\alpha +p^2+q^2=0$
$\Rightarrow 2{\alpha }^2-3p^2+(p^2+q^2)$
$D>09p^2-4.2(p^2+q^2)>0$
$\Rightarrow p^2>8^2$