If they made a sketch, they could have stated the problem more clearly.
The parabola is "horizontal", vertex at (0,0), opens to the right.
| P o *
| o *
| o* (p,q)
-o- - - - - - * - - - - - - - - -
The tangent at has its x-intercept at
Prove that is bisected by the y-axis.
We have: .
At , the slope of the tangent is: .
The equation of the tangent is: .
Since , we have: .
Let , the x-intercept is: .
Let , the y-intercept is: . .
Since , then
. . Substitute into : .
And is indeed the midpoint of and