Question

Find the equation of the hyperbola satisfying the give conditions: Foci, the latus rectum is of length 8.

Answer 1

Foci, the latus rectum is of length 8.

Here, the foci are on the x-axis.

Therefore, the equation of the hyperbola is of the form.

Since the foci are, c =.

Length of latus rectum = 8

We know that a² + b² = c².

∴a² + 4a = 45

⇒ a² + 4a – 45 = 0

⇒ a² + 9a – 5a – 45 = 0

⇒ (a + 9) (a – 5) = 0

⇒ a = –9, 5

Since a is non-negative, a = 5.

∴b² = 4a = 4 × 5 = 20

Thus, the equation of the hyperbola is.