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10-2. Parabola, Ellipse, Hyperbola
medium
Eccentricity of the ellipse $4{x^2} + {y^2} - 8x + 2y + 1 = 0$ is
A
$1/\sqrt 3 $
B
$\sqrt 3 /2$
C
$1/2$
D
None of these
Solution
(b) $4{x^2} – 8x + {y^2} + 2y + 1 = 0$
==> ${(2x – 2)^2} + {(y + 1)^2} = – 1 + 4 + 1$
==> $\frac{{{{(x – 1)}^2}}}{1} + \frac{{{{(y + 1)}^2}}}{4} = 1$
==> $e = \sqrt {1 – \frac{1}{4}} $
==> $e = \frac{{\sqrt 3 }}{2}$.
Standard 11
Mathematics
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