JEE Main & Advanced
Mathematics
Conic Sections
Question Bank
Self Evaluation Test - Conic Sections
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