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Find the Values of an Ellipse with the given equation

by Zachary
(CA, USA)











































How do i find these values? (see picture for equation and questions)

Comments for Find the Values of an Ellipse with the given equation

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May 11, 2012
Values of an Ellipse
by: Staff


Question:

by Zachary
(CA, USA)

How do i find these values? (see picture for equation and questions)


Answer:

x²/b² + y²/a² = 1

since a > b, this is a vertical ellipse. The major axis is vertical, and the minor axis is horizontal.

Center at (0, 0)

Vertices of major axis: (0, a) and (0, -a)

Vertices of minor axis: (b, 0) and (-b, 0)

Foci: (0, c) and (0, -c)

c² = a² - b²

c = √(a² - b²)

--------------------------------------------

x²/4² + y²/5² = 1


since 5 > 4, this is a vertical ellipse. The major axis is vertical, and the minor axis is horizontal.

Center at (0, 0)

Vertices of major axis: (0, 5) and (0, -5)

Vertices of minor axis: (2, 0) and (-2, 0)


c² = a² - b²

c = √(a² - b²)

c = √(5² - 4²)

c = √(25 - 16)

c = √(9)

c = ±3



Foci: (0, 3) and (0, -3)








Thanks for writing.

Staff
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