Question
Question: If the latusrectum through one focus subtends a right angle at the farther vertex of the hyperbola, ...
If the latusrectum through one focus subtends a right angle at the farther vertex of the hyperbola, then the eccentricity is
A
4
B
3
C
2
D
2
Answer
2
Explanation
Solution
From the diagram
ab2=a+ae
b2 = a2(1+e)
a2(e2 – 1) = a2(1+e)
e2 – e –2 = 0
⇒ e = 2.