Question

A chord is drawn on the parabola $y^2=8x$ through the vertex of the parabola and a point P. If P(x',y') satisfies the condition $y^{\prime 2}=8x^{\prime }$,then what is the midpoint of the chord.

• A. (2x',2y')
• B.
• C. (x',2y')
• D. (2x',y')

Answer 1

The correct option is B

The given parabola is $y^2=8x$. Its given that point P satisfies the condition $y^{\prime 2}=8x^{\prime }$.

This is same as saying that P lies on the parabola.

Then we obtain the chord OP as in the figure.

So midpoint of chord $OP=(\frac{x^{\prime }}{2},\frac{y^{\prime }}{2})$