Question

The area of the triangle formed by the lines joining vertex of the parabola x² = 12y to the extremities of its latus rectum is ______.

Options

• 18 sq units

• 38 sq units

• 12 sq units

• 28 sq units

Answer 1

The area of the triangle formed by the lines joining vertex of the parabola x² = 12y to the extremities of its latus rectum is 18 sq units.

Explanation:

Equation of parabola, x² = 12y

Length of latus rectum = 12

∴ AB = 12

Focus of parabola = (0, 3)

∴ OD = 3

Area of ΔOAB = `1/2 xx "OD" xx "AB"`

`= 1/2 xx 3 xx 12`

= 18 sq units