College Algebra Problems With Answers sample 10 : Equation of Hyperbola

College algebra problems on the equations of hyperbolas are presented.
Detailed solutions are at the bottom of the page.

Problem 1

Find the transverse axis, the center, the foci and the vertices of the hyperbola whose equation is
x^{ 2} / 4 - y^{ 2} / 9 = 1

Problem 2

Find the transverse axis, the center, the foci and the vertices of the hyperbola whose equation is
16 y^{ 2} - x^{ 2} = 16

Problem 3

Find the equation of a hyperbola that has the y axis as the transverse axis, a center at (0 , 0) and passes through the points (0 , 5) and (2 , 5√2).

Problem 4

Find the equation of a hyperbola whose vertices are at (0 , -3) and (0 , 3) and has a focus at (0 , 5).

Problem 5

Find the asymptotes of the parabolas given by the equations:
a) x^{ 2} / 4 - y^{ 2} / 36 = 1
b) y^{ 2} - 49 x^{ 2} = 49

Problem 6

Find the equation of a hyperbola with vertices at (0 , -7) and (0 , 7) and asymptotes given by the equations y = 3x and y = - 3x.

Problem 7

Find the equation of a hyperbola with foci at (-2 , 0) and (2 , 0) and asymptotes given by the equation y = x and y = -x.

Problem 8

Write the equation of a hyperbola with foci at (-1 , 0) and (1 , 0) and one of its asymptotes passes through the point (1 , 3).

Problem 9

Write the equation of a hyperbola with the x axis as its transverse axis, point (3 , 1) lies on the graph of this hyperbola and point (4 , 2) lies on the asymptote of this hyperbola.

Problem 10

Find the equation of each parabola shown below. The graphs in b) and c) also shows the asymptotes.
a)
b)
c)