Question

Find the area of the triangle formed by the line joining the vertex of the parabola x² = 12y to the end points of latus rectum.

Answer 1

Given equation of the parabola is x² = 12y.

Comparing this equation with x² = 4by, we get

4b = 12

∴ b = 3

∴ The co-ordinates of focus are S(0, b), i.e., S(0, 3)

End points of the latus rectum are L(2b, b) and L′(– 2b, b),

i.e., L(6, 3) and L′(– 6, 3)

Also l(LL′) = length of latus rectum

= 4b

= 12

l(OS) = b = 3

Area of the ΔOLL′ = `1/2 xx l("LL"^′) xx l("OS")`

= `1/2 xx 12 xx 3`

∴ Area of the ΔOLL’ = 18 sq. units.