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 length of transverse axis is 8 and distance between foci is 10.
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 = 8 ⇒ 2a = 8 ⇒ a = 4 ⇒ a² = 16 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 ⇒ b² = 25 – 16 = 9 The required equation of hyperbola is \(\frac {x^2}{16} - \frac {y^2}{9}=1\)

Find the equation of the hyperbola referred to its principal axes: Whose length of transverse axis is 8 and distance between foci is 10.

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 = 8

⇒ 2a = 8

⇒ a = 4

⇒ a² = 16

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

⇒ b² = 25 – 16 = 9

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