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What is the area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12 y$ to the ends of the latus rectum?
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Verified Answer
The correct answer is:
18 square units
Given parabola is $\mathrm{x}^{2}=12 y$ which is of the form $\mathrm{x}^{2}=4 a y$.
$\Rightarrow 4 a=12 \Rightarrow a=3$
Now, $L M$ is the latus rectum whose length $=4 a=4 \times 3$
=12
So, area of $\Delta L M V=\frac{1}{2} \times L M \times V F$.
$=\left(\frac{1}{2} \times 12 \times 3\right)$ sq. unit
$=18$ square unit
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