Two points and are suspected to lie on the same parabola of the form .

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Two points

P(6,8)

and

Q(24,16)

are suspected to lie on the same parabola of the form

y^{2}=4ax

. (i) Using the coordinates of

P

, determine the value of

a

. (ii) Verify whether the same value of

a

also satisfies the coordinates of

Q

. (iii) If your verification in part (ii) is affirmative, find the abscissa(s) of the point(s) on the parabola whose ordinate is

-8