Practice identifying, graphing, and analyzing circles and ellipses using standard form equations and geometric properties.
Read each problem carefully. Show your work and use correct mathematical notation for equations, centers, radii, vertices, and foci.
Writing equations and analyzing key features
Math - Grade 9-12
- 1
Write the standard form equation of a circle with center (2, -3) and radius 5.
- 2
Find the center and radius of the circle x^2 + y^2 - 6x + 10y + 9 = 0.
- 3
Determine whether the equation (x + 1)^2 + (y - 4)^2 = 49 represents a circle. If it does, state its center and radius.
- 4
Write the equation of a circle whose diameter has endpoints (-2, 1) and (6, 1).
- 5
A circle has center (0, 0) and passes through the point (8, 6). Write its equation.
- 6
State the center, vertices, co-vertices, and foci of the ellipse (x - 3)^2/25 + (y + 2)^2/9 = 1.
- 7
Write the standard form equation of an ellipse with center (0, 0), horizontal major axis, a = 6, and b = 4.
- 8
Find the center and lengths of the major and minor axes of the ellipse x^2/49 + y^2/9 = 1.
- 9
Determine whether the ellipse (x + 2)^2/16 + (y - 5)^2/36 = 1 has a horizontal or vertical major axis. Then state its vertices.
- 10
For the ellipse x^2/64 + y^2/48 = 1, find the value of c and the coordinates of the foci.
- 11
Write the equation of an ellipse centered at (1, -2) with vertical major axis, a = 7, and b = 3.
- 12
Complete the square to rewrite 4x^2 + 4y^2 - 16x + 8y - 20 = 0 in standard form. Then identify the graph.
- 13
An ellipse has center (0, 0), vertices at (0, 9) and (0, -9), and co-vertices at (4, 0) and (-4, 0). Write its equation.
- 14
A circle is tangent to the x-axis and has center (3, 5). Write the equation of the circle.
- 15
Compare the equations x^2/25 + y^2/25 = 1 and x^2/25 + y^2/9 = 1. Identify which graph is a circle and which is an ellipse, and explain why.