The area of the triangle formed by the lines joining vertex of the parabola $x^{2}=12 y$ to the extremities…
The area of the triangle formed by the lines joining vertex of the parabola $x^{2}=12 y$
to the extremities of its latus rectum is
- 38 sq. units
- 18 sq. units
- 12 sq. units
- 28 sq. units
Solution
$x^{2}=12 y \Rightarrow 4 b=12 \Rightarrow b=3$
Co-ordinates of latus return are $(\pm 2 b, b)$
$\therefore \mathrm{L}_{1} \equiv(6,3)$ and $\mathrm{L}_{2} \equiv(-6,3)$
Coordinates of focus $S \equiv(0,3)$
$\therefore \mathrm{A}\left(\Delta \mathrm{OL}_{1} \mathrm{~L}_{2}\right)=\frac{1}{2} \times 12 \times 3=18$
Asked in: MHT CET 2020 (19 Oct Shift 2)
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