The eccentricity of the hyperbola 25x-9y-144 is34 34123 3(d)34

1.	The eccentricity of the hyperbola 25x-9y-144 is34 34123 3(d)34
Answer» The given equation is (25x^2)/144 – (9y^2)/144 = 1 or [(x^2)/(12/5)^2] – [(y^2)/(12/3)^2] = 1 On comparing this equation with the standard equation of hyperbola [(x^2)/(a^2)] – [(y^2)/(b^2)] = 1 i.e., we obtain a = 12/5 and b = 12/3 We know that a^2 + b^2 = c^2 c^2 = 144/25 + 144/9c^2 = 144(34)/25*9c = 4 root(34)/5 Therefore, Eccentricity, e = c/a = 4 root(34)/5 /(12/5)= root(34)/3 (b) is correct option

Answer»

The given equation is (25x^2)/144 – (9y^2)/144 = 1

[(x^2)/(12/5)^2] – [(y^2)/(12/3)^2] = 1

On comparing this equation with the standard equation of hyperbola [(x^2)/(a^2)] – [(y^2)/(b^2)] = 1 i.e., we obtain a = 12/5 and b = 12/3

We know that a^2 + b^2 = c^2

c^2 = 144/25 + 144/9c^2 = 144(34)/25*9c = 4 root(34)/5

Therefore,

Eccentricity, e = c/a = 4 root(34)/5 /(12/5)= root(34)/3

(b) is correct option

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