Question

The area of the triangle formed by the lines joining the vertex of the parabola x² = 20y to the end of its latus rectum is

Options

• 100 sq. units

• 20 sq. units

• 40 sq. units

• 50 sq. units

Answer 1

50 sq. units

Explanation:

Given parabola is x² =  20y

∴ a = 5, vertex = (0, 0)
Focus = (0, 5)
Latus rectum = 4a = 20

∴ Ends of latus rectum are A(−10, 5) and B(10, 5)

\[\mathrm{A}(\Delta\mathrm{AOB})=\frac{1}{2}\times\mathrm{AB}\times\mathrm{OC}\]

\[=\frac{1}{2}\times20\times5\]

= 50 sq. units.