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Question: Eccentricity of hyperbola \(\frac{x^{2}}{a^{2}}–\frac{y^{2}}{b^{2}}\) = 1 if latus rectum subtend 90...

Eccentricity of hyperbola x2a2–y2b2\frac{x^{2}}{a^{2}}–\frac{y^{2}}{b^{2}} = 1 if latus rectum subtend 90ŗ at farthest vertex:

A

2\sqrt{2}

B

2

C

32\frac{3}{2}

D

None of these

Answer

2

Explanation

Solution

tan 450 = b2/aa+ae\frac{b^{2}/a}{a + ae}

1 = b2/a21+e\frac{b^{2}/a^{2}}{1 + e} = e2–1e+1\frac{e^{2}–1}{e + 1}

Ž 1 = e – 1

Ž e = 2