Hello, Rimas!
If they made a sketch, they could have stated the problem more clearly. Code:

 P o *
 o *
 o* (p,q)
o *
o *
o 
o      *         
Q 
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The parabola is "horizontal", vertex at (0,0), opens to the right.
The tangent at has its xintercept at
Prove that is bisected by the yaxis.
We have: .
At , the slope of the tangent is: .
The equation of the tangent is: .
Since , we have: .
Let , the xintercept is: .
Let , the yintercept is: . .[1]
Since , then
. . Substitute into [1]: .
And is indeed the midpoint of and