Question

Find the equation of
Hyperbela foci (o, +3)
latus Rectum =36​

Answer 1

Foci = be = 3   , e = 3/b -- (2)

Here value of b>a

Latus rectum = 2a²/b

              36 = 2a²/b

               36b = 2a²

                  18b = a² -- (1)

We know that e² = 1 + a²/b²

                     substituting values from equation 1 & 2

                    we get quadratic equation -->  b² + 18b - 9

 solving the equation we get root in terms of irrational number

                     There is some error in the question i guess

but if foci and latus rectum is given , then this is the method to find values of a nd b in hyperbola equation