Equation of a hyperbola, whose foci are (5, 0) and (-5, 0) and length of whose conjugate axis is 8 ,

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10-2. Parabola, Ellipse, Hyperbola

easy

The equation of a hyperbola, whose foci are $(5, 0)$ and $(-5, 0)$ and the length of whose conjugate axis is $8$, is

A

$9{x^2} - 16{y^2} = 144$

B

$16{x^2} - 9{y^2} = 144$

C

$9{x^2} - 16{y^2} = 12$

D

$16{x^2} - 9{y^2} = 12$

Solution

(b) $b = 4$

$⇒$ $2ae = 10$

$⇒$ $16 = 25 – {a^2}$

$⇒$ $a = 3$

Hence the hyperbola is $16{x^2} – 9{y^2} = 144$.

Standard 11

Mathematics

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