Conics - Ellipses
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
FREE Resource
Student preview
15 questions
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1.
FLASHCARD QUESTION
Front
What is the standard form of the equation of an ellipse centered at the origin with a horizontal major axis?
Back
The standard form is \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) where \( a > b \).
Tags
CCSS.HSG.GPE.A.1
2.
FLASHCARD QUESTION
Front
What is the standard form of the equation of an ellipse centered at the origin with a vertical major axis?
Back
The standard form is \( \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 \) where \( a > b \).
Tags
CCSS.HSG.GPE.A.1
3.
FLASHCARD QUESTION
Front
What do the variables 'a' and 'b' represent in the standard equation of an ellipse?
Back
'a' represents the semi-major axis length, and 'b' represents the semi-minor axis length.
Tags
CCSS.HSG.GPE.A.1
4.
FLASHCARD QUESTION
Front
How do you find the foci of an ellipse?
Back
The foci are located at \( (\pm c, 0) \) for horizontal ellipses and \( (0, \pm c) \) for vertical ellipses, where \( c = \sqrt{a^2 - b^2} \).
Tags
CCSS.HSG.GPE.A.1
5.
FLASHCARD QUESTION
Front
If the foci of an ellipse are 40 feet apart, what is the distance from the center to each focus?
Back
The distance from the center to each focus is 20 feet.
6.
FLASHCARD QUESTION
Front
What is the relationship between the lengths of the axes and the foci in an ellipse?
Back
The distance between the foci is less than the length of the major axis.
7.
FLASHCARD QUESTION
Front
What is the length of the major axis if the semi-major axis is 'a'?
Back
The length of the major axis is \( 2a \).
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