Hyperbola Solver

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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






 

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