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10-2. Parabola, Ellipse, Hyperbola
easy
The distance between the foci of the ellipse $3{x^2} + 4{y^2} = 48$ is
A
$2$
B
$4$
C
$6$
D
$8$
Solution
(b) $\frac{{{x^2}}}{{(48/3)}} + \frac{{{y^2}}}{{(48/4)}} = 1$
${a^2} = 16,\;{b^2} = 12$
$e = \sqrt {1 – \frac{{{b^2}}}{{{a^2}}}} = \frac{1}{2}$
Distance is $2ae = 2 \cdot 4 \cdot \frac{1}{2} = 4$.
Standard 11
Mathematics