Question

Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

Answer 1

Given:Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).To find:The equation of hyperbola.Solution:We have, directrices at y = ±2 so this hyparabola is along the y-axis.The standard form of hyperbola is ...(i)where, (h,k) is center, foci are and directrix are .On comparing foci, we getOn comparing directrix we getNow,Putting , we get Therefore, the equation of hyperbola is .