Question

If $(x_1,y_1)$ and $(x_2,y_2)$ and ends of a focal chord of the parabola $y^2=4ax$, then square of G.M. of $x_1$ and $x_2$ is?

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

Answer 1

The correct option is C $a^2$

Parabola:$y^2=4ax$

Let $(x_1,y_1)=(a{t}^2,2at)$

$(x_2,y_2)$ is another end of focal chord of the Parabola.

$\therefore (x_2,y_2)=(\frac{a}{t^2},\frac{-2a}{t})$

Square of GM of $x_1$ and $x_2$ is

$=(\sqrt{a{t}^2\times \frac{a}{t^2}}{)}^2=a^2$

Hence the GM of $x_1$ and $x_2$ is $a^2$.