Conic-Sections Question 559
Question: 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?
Options:
A) 9 square units
B) 12 square units
C) 14 square units
D) 18 square units
Show Answer
Answer:
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. $ $ =( \frac{1}{2}\times 12\times 3 ) $ sq. unit = 18 square unit
BETA
