If the chord joining the points P_1(t_1) and P_2(t_2) on the parabola y^2=12x subtends a r…

Question

If the chord joining the points $P_1(t_1)$ and $P_2(t_2)$ on the parabola $y^2=12x$ subtends a right angle at the vertex of the parabola, then $x_1x_2-y_1y_2$ is equal to \_\_\_\_\_\_\_\_.

Accepted Answer

Here $a=3$. A chord subtending a right angle at the vertex of $y^2=4ax$ satisfies $t_1t_2=-4$.

$$x_1x_2=a^2(t_1t_2)^2=9\times16=144,\qquad y_1y_2=4a^2t_1t_2=4\times9\times(-4)=-144.$$

$x_1x_2-y_1y_2=144-(-144)=288.$

Solutions · 1