Find the equation of the hyperbola referred to its principal axes: W

1.	Find the equation of the hyperbola referred to its principal axes: Whose lengths of transverse and conjugate axes are 6 and 9 respectively.
Answer» Let the required equation of hyperbola be \(\frac{x^2}{a^2} - \frac {y^2}{b^2} = 1\) Length of transverse axis = 2a Given, length of transverse axis = 6 ⇒ 2a = 6 ⇒ a = 3 ⇒ a² = 9 Length of conjugate axis = 2b Given, length of conjugate axis = 9 ⇒ 2b = 9 ⇒ b = 9/2 ⇒ b² = 81/4 The required equation of hyperbola is \(\frac {x^2}{9} - \frac {y^2}{\frac{81}{4}}=1\) i.e., \(\frac {x^2}{9} - \frac {4y^2}{81}=1\)

Find the equation of the hyperbola referred to its principal axes: Whose lengths of transverse and conjugate axes are 6 and 9 respectively.

Answer»

Let the required equation of hyperbola be \(\frac{x^2}{a^2} - \frac {y^2}{b^2} = 1\)

Length of transverse axis = 2a

Given, length of transverse axis = 6

⇒ 2a = 6

⇒ a = 3

⇒ a² = 9

Length of conjugate axis = 2b

Given, length of conjugate axis = 9

⇒ 2b = 9

⇒ b = 9/2

⇒ b² = 81/4

The required equation of hyperbola is \(\frac {x^2}{9} - \frac {y^2}{\frac{81}{4}}=1\)

i.e., \(\frac {x^2}{9} - \frac {4y^2}{81}=1\)