Equation of Hyperbola Tutors

Equation of Hyperbola Tutors 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 formy2/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 isx2/9- 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 isy2/25- x2/64= 1 We can write this asy2/5- 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).