Question

Find a equation of the parabola with vertex at (0,0) passing through (5,2) and symmetric with respect to y-axis.

Answer 1

The equatipn of the parabola is 25y^2 = 4x

Answer 2

Given vertex is origin and axis is y-axis, the equation is of the form x2=4ay of x2=-4ay

Since the parabola passes through (5,2) the equation is of the form x2=4ay which means that 52=4×a×2

→a=25/8

Therefore, the equation of the parabola is x2=4 25/8 y

=25/2y