question_answer

What is the area of the triangle formed by the lines joining the vertex of the parabola \[{{x}^{2}}=12y\] to the ends of the latus rectum?

A) 9 square units

B) 12 square units

C) 14 square units

D) 18 square units

Correct Answer: D

Solution :

[d] Given parabola is \[{{x}^{2}}=12y\] which is of the form \[{{x}^{2}}=4ay.\] \[\Rightarrow 4a=12\Rightarrow a=3\] Now, LM is the latus rectum whose length \[=4a=4\times 3=12\] So, area of \[\Delta LMV=\frac{1}{2}\times LM\times VF.\] \[=\left( \frac{1}{2}\times 12\times 3 \right)\] sq. unit = 18 square unit