Equation of hyperbola referred to axis as axes of co-ordinate and whose distance between foci is 16

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10-2. Parabola, Ellipse, Hyperbola

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The equation of the hyperbola referred to the axis as axes of co-ordinate and whose distance between the foci is $16$ and eccentricity is $\sqrt 2 $, is

A

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

B

${x^2} - {y^2} = 32$

C

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

D

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

Solution

(b) According to question, Transverse axis = Conjugate axis

Given that, $e = \sqrt 2 ,\,2ae = 16$;

$a = 4\sqrt 2 $

Therefore, equation of hyperbola is ${x^2} – {y^2} = 32.$

Standard 11

Mathematics

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