Find the area of the triangle formed by the lines joining the vertex of the parabola `x^(2) = 8y` to the ends of its latus rectum.

Explanation

The given equation of the parabola is of the form `x^(2) = 4ay`
`rArr 4a = 8`
i.e., a = 2
`therefore` The length of the latus rectum is 4a i.e., 8
Now, In `triangleOAB`,
AB = 8 units and OF = 2 units
`therefore` Area of the triangle formed by the lines joining the vertex of the given parabola to the ends of the latus rectum is :
`(1)/(2) xx AB xx OF`
i.e., `(1)/(2) xx 8 xx 2 = 8` units.