College Algebra Problems With Answers sample 10 : Equation of Hyperbola

A set of college algebra problems on the equation of hyperbolas are presented. The solutions are at the bottom of the page.

Find the transverse axis, the center, the foci and the vertices of the hyperbola whose equation is

x^{ 2} / 4 - y^{ 2} / 9 = 1

Find the transverse axis, the center, the foci and the vertices of the hyperbola whose equation is

16 y^{ 2} - x^{ 2} = 16

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).

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

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.

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.

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).

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.

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