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Question: The eccentricity of the hyperbola 9x<sup>2</sup> – 16y<sup>2</sup> –18x –64y – 199 = 0 is...

The eccentricity of the hyperbola

9x2 – 16y2 –18x –64y – 199 = 0 is

A

16/9

B

5/4

C

25/16

D

Zero

Answer

5/4

Explanation

Solution

(x1)216\frac{(x - 1)^{2}}{16}(y+2)29\frac{(y + 2)^{2}}{9}= 1

e = 1+b2a2\sqrt{1 + \frac{b^{2}}{a^{2}}}= 1+916\sqrt{1 + \frac{9}{16}}= 54\frac{5}{4}