Question

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Answer 1

Vertices (0, ±3), foci (0, ±5)
Here, the vertices are on the y-axis.
Therefore, the equation of the hyperbola is of the form Y²/a² - X²/b² =1.
Since the vertices are (0, ±3), a = 3.
Since the foci are (0, ±5), c = 5.
We know that a² + b² = c².
∴3² + b² = 5²
⇒ b² = 25 – 9 = 16
Thus, the equation of the hyperbola is Y²/9 - X²/16 =1.