Grade 12 Math: Ellipse Worksheet
This worksheet covers key concepts of ellipses, including their equations, foci, vertices, and eccentricity, suitable for Grade 12 Algebra students.
Includes
Standards
Ellipse Worksheet
Name:
Date:
Score:
Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following is the standard form equation of an ellipse centered at (h, k)?
(x-h)²/a² + (y-k)²/b² = 1
(x-h)²/a² - (y-k)²/b² = 1
(x-h)²/a² + (y-k)²/a² = 1
(x-h)²/b² + (y-k)²/a² = 0
2. What is the eccentricity of an ellipse?
The distance from the center to a vertex.
A measure of how 'stretched' the ellipse is.
The length of the minor axis.
The distance between the foci.
3. The two fixed points inside an ellipse are called the .
4. The longest diameter of an ellipse is called the axis.
5. Find the foci of the ellipse given by the equation (x²/25) + (y²/16) = 1.
6. Write the equation of an ellipse with foci at (±3, 0) and vertices at (±5, 0).
7. For an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant.
True
False
8. An ellipse with an eccentricity of 0 is a circle.
True
False
9. Graph the ellipse given by the equation (x²/9) + (y²/4) = 1. Clearly mark the center, vertices, and co-vertices.
10. Consider the ellipse with the equation ((x-1)²/16) + ((y+2)²/9) = 1. Identify its center, vertices, co-vertices, and foci. Then, sketch the graph.
Center:
Vertices:
Co-vertices:
Foci:
Related Worksheets
Perfect Square Trinomials
This worksheet focuses on identifying, factoring, and constructing perfect square trinomials, essential skills for Grade 12 Algebra.
Solving Square Root Equations
This worksheet focuses on solving square root equations, including identifying extraneous solutions, for Grade 12 Algebra students.
Finding Polynomial Functions from Graphs
Grade 12 math worksheet on determining polynomial functions given their graphs, focusing on roots, multiplicity, and end behavior.
Combining Polynomials Worksheet
Grade 12 math worksheet on combining polynomials, including addition, subtraction, multiplication, and division.
Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions (identities) or no solutions (contradictions) at a Grade 12 level.
Grade 12: Rearranging Equations
This worksheet focuses on rearranging complex algebraic equations to solve for specific variables, suitable for Grade 12 mathematics.
Grade 12: Rearranging Equations
This worksheet focuses on rearranging complex algebraic equations to solve for specific variables, suitable for Grade 12 mathematics.
Direct Variation Worksheet
A Grade 12 mathematics worksheet focusing on direct variation, including identifying direct variation, writing equations, and solving problems.