Hyperbola Solver

Hyperbola Solver Characteristic of different types of hyperbolas are given in the following table: x^2/a^2 y^2/b^2 = 1 y^2/a^2 x^2/b^2 =1 Transverse axis x- axis y- axis Conjugate axis y- axis x- axis Equation of transverse axis Y =0 X = 0 Equation of conjugate axis X = 0 Y = 0 Length of transverse axis 2 a unit 2 a unit Length of conjugate axis 2 b unit 2 b unit Coordinates of Centre (0, 0) (0, 0) Coordinate of vertices (a, 0) (0, a) Coordinates of foci (a e, 0) (0, ae) Distance between two foci 2 a e unit 2 a e unit Length of latus rectum 2 b^2 / a unit 2 b^2 / a unit Equations of latera recta x = a e y = a e Equations of directrices x = a / e Y = a / e Distance between two directrices 2 a / e unit 2 a / e unit Question1: - Find the length of the latus rectum of the hyperbola 9 y ^2 4 x^2 = 36. Solution: - 9 y ^2 4 x^2 = 36 Or, y^2/4 x^2/9 = 1 Comparing the above equation with the equation of hyperbola y^2/a^2 x^2/b^2 =1 we get, A^2= 24, therefore a =2 And b^2=9, therefore b =3 Length of its latus rectum: 2 b^2 / a = 2*3^2 / 2 = 9. Question 2: - For the same above parabola find the axes. Solution: -Transverse axis = 2a= 2*2=4 Conjugate axis = 2b= 2*3 = 6