Find the area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latus - rectum.

Given that we need to find the area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latus - rectum.

Comparing it with the standard form of parabola x² = 4by.

⇒ Vertex is 0(0, 0)

⇒ Ends of latus rectum is (2b, b), (- 2b, b)

⇒ 4b = 12

⇒ b = 3

⇒ Ends of latus rectum is (2(3), 3), (- 2(3), 3)

⇒ Ends of latus rectum is A(6, 3), B(- 6, 3)

We know that area of the triangle with the vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

⇒

⇒

⇒

⇒

⇒

⇒ A = 18sq.units.

∴The area of the triangle is 18 sq.units.