P is the point (ap^2 , 2ap) and Q the point (aq^2 , 2aq) on the parabola $\displaystyle y^2 = 4ax$. The cord PQ passes through the point (a,0)
a) Prove that pq = -1
I have no idea how to get started . Thanks in advance
You have 2 points. Determine the equation of the line which passes through these points: If you know $\displaystyle P_1(x_1 , y_1)$ and $\displaystyle P_2(x_2 , y_2)$ then the equation of the line $\displaystyle P_1P_2$ is:
$\displaystyle \dfrac{y-y_1}{x-x_1}= \dfrac{y_2-y_1}{x_2-x_1}$
Since this line has to pass through (a, 0) you only have to replace x by a and y by 0. Simplify!