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Question: If centre, vertex & focus of hyperbola are (2, 0) (4, 0) & (8, 0) then length of latus rectum...

If centre, vertex & focus of hyperbola are (2, 0) (4, 0) & (8, 0) then length of latus rectum

A

32

B

24

C

16

D

None of these

Answer

32

Explanation

Solution

Distance between centre & vertex = a = 2

Distance between foci & centre = ae = 6

Ž e = 3

b2 = a2(e2 – 1) = 4(9 – 1) = 32

Latus Rectum = 2b2a\frac{2b^{2}}{a} = 2×322\frac{2 \times 32}{2} = 32