Find the equation of the hyperbola with

Foci , passing through (2, 3)

Foci = & passing through (2, 3)

As

Also, a² = b² (e² - 1)

= b²e² - b²

=

= 10 - b²

General Equation of Hyperbola is

As, this hyperbola passed through (2, 3)

4b² - 9 (10 - b²) = -1(10 - b²) (b²)

4b² – 90 + 9b² = -10b² + b⁴

b⁴ - 23b² + 90 = 0

b⁴ - 18b² - 5b² + 90 = 0

b²(b² - 18)- 5 (b² - 18) = 0

(b² - 5) (b² - 18) =0

Either b² = 5 or b² = 18 (not possible, as a² + b² = 10)

a² + b² = 10

a² + 5 = 10

a² = 5

Hence, the required equation is .