Question

If the vertex = (2, 0) and the extremities of the latus rectum are (3, 2) and (3, –2) then the equation of the parabola is ______.

Options

• y² = 2x – 4

• x² = 4y – 8

• y² = 4x – 8

• x² = 2y – 4

Answer 1

If the vertex = (2, 0) and the extremities of the latus rectum are (3, 2) and (3, –2) then the equation of the parabola is `underlinebb(y^2 = 4x - 8)`.

Explanation:

Vertex = (2, 0) focus will be the midpoint of extremities of the latus rectum

∴ Focus = (3, 0)

∴ Distance between focus and vertex is a = 1

Since axis of the parabola is x-axis

∴ Its equation will be (y – 0)² = 4.1.(x – 2)

⇒ y² = 4(x – 2)

⇒ y² = 4x – 8