A point lies on a parabola whose equation is of the form

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

A point

P(5,6)

lies on a parabola whose equation is of the form

y^{2}=4ax

. (i) Verify that

P

satisfies an equation of this form and hence find the value of

a

. (ii) For this value of

a

, determine the coordinates of the focus and the equation of the directrix. (iii) Plot at least three suitable points (including

P

and its reflection in the x-axis) and sketch the corresponding parabola, indicating clearly its orientation.