Question

Find the equation of the hyperbola referred to its principal axes: Whose distance between foci is 10 and length of the conjugate axis is 6.

Answer 1

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

Length of conjugate axis = 2b 

Given, length of conjugate axis = 6 

⇒ 2b = 6 

⇒ b = 3 

⇒ b² = 9 

Distance between foci = 2ae 

Given, distance between foci = 10 

⇒ 2ae = 10 

⇒ ae = 5

⇒ a² e² = 25 

Now, b² = a² (e² – 1) 

⇒ b² = a² e² – a² 

⇒ 9 = 25 – a²

⇒ a² = 25 – 9 

⇒ a² = 16 

The required equation of hyperbola is \(\frac{x^2}{16} - \frac {y^2}{9} = 1\)