Find the area of the triangle formed by the lines joining the vertex of the parabola `x^2= 12 y`to the ends of its latus rectum.

Options

A. 12 sq. units
B. 14 sq. units
C. 16 sq. units
D. 18.sq. units

Answer

D

Explanation

we know that, latusrectum is a line perpendicular to the axis and passing through focus whose length is 4a.
given, x^(2)=12y, which of the from x^(2)=4ay`
`therefore4a=12= length of acb focus c=(0,3) `
`therefore` area of DeltaOAB=(1)/(2)xABxOC=(1)/(2)x12x3=6x3=18` sq units