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10-2. Parabola, Ellipse, Hyperbola
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The equation of the ellipse whose centre is $(2, -3)$, one of the foci is $(3, -3)$ and the corresponding vertex is $(4, -3)$ is
A
$\frac{{{{(x - 2)}^2}}}{3} + \frac{{{{(y + 3)}^2}}}{4} = 1$
B
$\frac{{{{(x - 2)}^2}}}{4} + \frac{{{{(y + 3)}^2}}}{3} = 1$
C
$\frac{{{x^2}}}{3} + \frac{{{y^2}}}{4} = 1$
D
None of these
Solution
(b) Foci $ = (3, – 3)$ $⇒$ $ae = 3 – 2 = 1$
Vertex $ = (4, – 3)$ $⇒$ $a = 4 – 2 = 2$
$⇒$ $e = \frac{1}{2}$
$⇒$ $b = a\sqrt {\left( {1 – \frac{1}{4}} \right)} = \frac{2}{2}\sqrt 3 = \sqrt 3 $
Therefore, equation of ellipse with centre $(2, – 3)$ is
$\frac{{{{(x – 2)}^2}}}{4} + \frac{{{{(y + 3)}^2}}}{3} = 1$.
Standard 11
Mathematics
