Ellipses and Circles Practice
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the standard form equation of an ellipse?
Back
The standard form equation of an ellipse is given by (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the semi-major axis, and b is the semi-minor axis.
2.
FLASHCARD QUESTION
Front
What are the vertices of an ellipse?
Back
The vertices of an ellipse are the points where the ellipse intersects its major axis. They are located at a distance 'a' from the center along the major axis.
3.
FLASHCARD QUESTION
Front
What are the co-vertices of an ellipse?
Back
The co-vertices of an ellipse are the points where the ellipse intersects its minor axis. They are located at a distance 'b' from the center along the minor axis.
4.
FLASHCARD QUESTION
Front
How do you find the eccentricity of an ellipse?
Back
The eccentricity (e) of an ellipse is calculated using the formula e = √(1 - (b²/a²)), where 'a' is the semi-major axis and 'b' is the semi-minor axis.
5.
FLASHCARD QUESTION
Front
What is the relationship between the lengths of the axes and the eccentricity of an ellipse?
Back
As the eccentricity of an ellipse increases (closer to 1), the ellipse becomes more elongated, and the lengths of the axes differ more significantly.
6.
FLASHCARD QUESTION
Front
What is the general shape of an ellipse?
Back
An ellipse is a closed curve that resembles a flattened circle, defined as the set of points where the sum of the distances to two fixed points (foci) is constant.
7.
FLASHCARD QUESTION
Front
How do you graph an ellipse given its equation?
Back
To graph an ellipse, identify the center, vertices, and co-vertices from the equation, then plot these points and sketch the curve smoothly connecting them.
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