Question

Find the equation of the parabola that satisfies the following condition:

Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.

Answer 1

Since the vertex is (0, 0) and the parabola is symmetric about the y-axis, the equation of the parabola is either of the form x² = 4ay or x² = –4ay.

The parabola passes through point (5, 2), which lies in the first quadrant.

Therefore, the equation of the parabola is of the form x² = 4ay, while point (5, 2) must satisfy the equation x² = 4ay.

∴ (5)² = 4 × a × 2 = 25 = 8a = a = `25/8`

Thus, the equation of the parabola is

x² = `4 (25/8)y`

2x² = 25y