MCQ
The eccentricity of the hyperbola $5{x^2} - 4{y^2} + 20x + 8y = 4$ is
- A$\sqrt 2 $
- ✓$\frac{3}{2}$
- C$2$
- D$3$
✓
Answer
Correct option: B.
$\frac{3}{2}$
b
(b) Given equation of hyperbola is $5{x^2} - 4{y^2} + 20x + 8y = 4$
(b) Given equation of hyperbola is $5{x^2} - 4{y^2} + 20x + 8y = 4$
$5{(x + 2)^2} - 4\,{(y - 1)^2} = 20$ ==> $\frac{{{{(x + 2)}^2}}}{4} - \frac{{{{(y - 1)}^2}}}{5} = 1$
From ${b^2} = {a^2}({e^2} - 1)$, $5 = 4({e^2} - 1)$
$ \Rightarrow {e^2} = 9/4 $
$\Rightarrow e = 3/2$.
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