Question

The co-ordinates of the ends of a focal chord of a parabola $y^2=4ax$ are $(x_1,y_1)$ and $(x_2,y_2)$, then $x_1{x}_2+y_1{y}_2$ is equal to

• A. $2a^2$
• B. $4a^2$
• C. $-3a^2$
• D. $-a^2$

Answer 1

The correct option is C $-3a^2$

Let $x_1=a{t}^2$ and $y_1=2at$, then
$x_2=\frac{a}{t^2}$ and $y_2=\frac{-2a}{t}$
$\Rightarrow x_1{x}_2+y_1{y}_2=-3a^2$