College Algebra Problems With Answers sample 8 : Equation of Ellipse

A set of college algebra problems on the equation of ellipses are presented.
Problems on ellipses with detailed solutions are included in this site. The solutions are at the bottom of the page.

What is the major axis and its length for the following ellipse?

(1/9) x^{ 2} + (9/25) y^{ 2} = 1/25

An ellipse is given by the equation

8x^{ 2} + 2y^{ 2} = 32

.

Find

a) the major axis and the minor axis of the ellipse and their lengths,

b) the vertices of the ellipse,

c) and the foci of this ellipse.

Find the equation of the ellipse whose center is the origin of the axes and has a focus at (0 , -4) and a vertex at (0 , -6).

Find the equation of the ellipse whose foci are at (0 , -5) and (0 , 5) and the length of its major axis is 14.

An ellipse has the x axis as the major axis with a length of 10 and the origin as the center. Find the equation of this ellipse if the point (3 , 16/5) lies on its graph.

An ellipse has the following equation

0.2x^{ 2} + 0.6y^{ 2} = 0.2

.

a) Find the equation of part of the graph of the given ellipse that is to the left of the y axis.

b) Find the equation of part of the graph of the given ellipse that is below the x axis.

An ellipse is given by the equation

(x - 1)^{ 2} / 9 + (y + 4)^{ 2} / 16 = 1

.

Find

a) its center,

a) its major and minor axes and their lengths,

b) its vertices,

c) and the foci.

Find the equation of the ellipse whose foci are at (-1 , 0) and (3 , 0) and the length of its minor axis is 2.

An ellipse is defined by its parametric equations as follows

x = 6 sin(t) and y = 4 cos(t)

Find the center, the major and minor axes and their lengths of this ellipse.