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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\sqrt{3}

C

2

D

2\sqrt{2}

Answer

2

Explanation

Solution

From the diagram

b2a=a+ae\frac{b^{2}}{a} = a + ae

b2 = a2(1+e)

a2(e2 – 1) = a2(1+e)

e2 – e –2 = 0

⇒ e = 2.