Question

Find the equation of the hyperbola satisfying the give conditions: Foci, passing through (2, 3)

Answer 1

Foci, passing through (2, 3)

Here, the foci are on the y-axis.

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

Since the foci are, c =.

We know that a² + b² = c².

∴ a² + b² = 10

⇒ b² = 10 – a² … (1)

Since the hyperbola passes through point (2, 3),

From equations (1) and (2), we obtain

In hyperbola, c > a, i.e., c² > a²

∴ a² = 5

⇒ b² = 10 – a² = 10 – 5 = 5

Thus, the equation of the hyperbola is.