Question

The area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latusrectum is
(a) 12 sq. units
(b) 16 sq. units
(c) 18 sq. units
(d) 24 sq. units

Answer 1

The given equation of parabola is
x² = 12y ...(1)
which is of the form x² = 40y --(2)
∴ comparing (1) and (2),
we get 12y = 40y
i.e. a = 3

Let P be the focus for parabola,
i.e. OP = 3
Length of lotus rectum is 4a
= 4 × 3
= 12
$\begin{array}{rcl}\therefore \mathrm{Area}\mathrm{of}\mathrm{triangle}\mathrm{AOB}& =& \frac{1}{2}\times \mathrm{Base}\times \mathrm{Altitude}\\ & =& \frac{1}{2}\times AB\times OP\\ & =& \frac{1}{2}\times 12\times 3\end{array}$
i.e. Area of triangle formed = 18 square units.

Hence, the correct answer is option C.