Equation of Hyperbola

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We know hyperbola is a type of smooth curve in a plane. We know the equation of parabola that is

x2/a2 - y2/b2 = 1. We have two vertices to a hyperbola. One is at (a, 0) and another one is (-a, 0). If the equation is in the

form y2/b2 - x2/a2 = 1. We have two vertices to a hyperbola, those are (0, b) 


Example 1: Find the vertices of the parabola x2/9 -  y2/16 = 1

Solution: The given equation of parabola is x2/9 -  y2/16 = 1

We can write this as x2/32-  y2/42 = 1

First we need to compare the given equation with  x2/a2 - y2/b2 = 1

From this we can write, a = 3 and b = 4

We know the vertices of a hyperbola those are, (a, 0) and (-a, 0)

Therefore the vertices are (3, 0) and (-3, 0).

Example 2: Find the vertices of the parabola y2/25 -  x2/64 = 1

Solution: The given equation of parabola is y2/25 -  x2/64 = 1

We can write this as y2/5 -  x2/8  = 1

First we need to compare the given equation with y2/b2 -  x2/a2 = 1

From this we can write, a = 8 and b = 5

We know the vertices of a hyperbola those are, (0, b) and (0, -b)

Therefore, the vertices are (0, 5) and (0, -5).


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