FIND EQUATIONS OF ASYMPTOTES OF HYPERBOLA WORKSHEET

Find the coordinates of the vertices, foci and the equation of asymptotes for the hyperbola with the given equation. Then graph the hyperbola :

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

x² - 36y² = 36

Solution

Problem 4 :

5x² - 4y² - 40x - 16y  - 36 = 0

Solution

Problem  5 :

Comets that pass by Earth only once may follow hyperbolic paths. Suppose a comet's path is modeled by a branch of the hyperbola with the equation 

(y² / 225) - (x² / 400) = 1

Find the coordinates of the vertices and foci and the equation of asymptotes for the hyperbola.

Solution

Answer Key

1)

a = 3√2 and b = 2√5

Vertices : (0, 0)

Foci : (0, √38) and (0, -√38)

Equation of asymptotes :

2)

a = 2√5 and b = 5

Vertices : (1, -6)

Foci : (1, -6+3√5) and (1, -6-3√5)

Equation of asymptotes :

3)  

a = 6 and b = 1

Vertices : (0, 0)

Foci : Foci are (√37, 0) and (-√37, 0)

Equation of asymptotes :

4)

a = 2√5 and b = 5

Vertices : (4, -2)

Foci : (4+3√5, -2) and (4-3√5, -2)

Equation of asymptotes :

5) 

a = 25 and b = 20

Vertices : (0, 0)

Foci :(0, 25) and (0, -25)

Equation of asymptotes :

y = -4x/5 and y = 4x/5