# Thread: Help with solving a parabola

1. ## Help with solving a parabola

P is the point (ap^2 , 2ap) and Q the point (aq^2 , 2aq) on the parabola $y^2 = 4ax$. 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

2. ## Re: Help with solving a parabola

Originally Posted by womatama
P is the point (ap^2 , 2ap) and Q the point (aq^2 , 2aq) on the parabola $y^2 = 4ax$. 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
Start by drawing a diagram. Have you done that?

3. ## Re: Help with solving a parabola

Originally Posted by womatama
P is the point (ap^2 , 2ap) and Q the point (aq^2 , 2aq) on the parabola $y^2 = 4ax$. 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 $P_1(x_1 , y_1)$ and $P_2(x_2 , y_2)$ then the equation of the line $P_1P_2$ is:

$\dfrac{y-y_1}{x-x_1}= \dfrac{y_2-y_1}{x_2-x_1}$

Since this line has to pass through (a, 0) you only have to replace x by a and y by 0. Simplify!