Radius of director circle of hyperbola frac{{{x^2}}}{{{a^2}}} - frac{{{y^2}}}{{{b^2}}} = 1 , is

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10-2. Parabola, Ellipse, Hyperbola

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The radius of the director circle of the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, is

A

$a - b$

B

$\sqrt {a - b} $

C

$\sqrt {{a^2} - {b^2}} $

D

$\sqrt {{a^2} + {b^2}} $

Solution

(c) Equation of director-circle of the hyperbola

$\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1$ is ${x^2} + {y^2} = {a^2} – {b^2}$

So, radius $ = \sqrt {{a^2} – {b^2}} $.

Standard 11

Mathematics

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