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Question 206846: Id have a question, did I understand/do this problem right?
Problem; What is the equation of the ellipse with foci at (0,-4) and (0,4) and the sum of its focal radii being 10?
My answer; 2a=10 a=5(sum of focal radii)
(0+0/2, 4+4/2)= (0,4)
c=4 b^2= a^2-c^2= 25-16=9
equation of the ellipse is;
(x-0)^2/25 + (y-4)^2/9=1
(Is this right?)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Which definition does your book use?
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This term has distinctly different definitions for different authors.
Usage 1: For some authors, this refers to the distance from the center to the focus for either an ellipse or a hyperbola. This definition of focal radius is usually written c.
Usage 2: For other authors, focal radius refers to the distance from a point on a conic section to a focus. In this case the focal radius varies depending where the point is on the curve (unless the conic in question is a circle). If there are two foci then there are two focal radii.
Note: Using this second definition, the sum of the focal radii of an ellipse is a constant. It is the same as the length of the major diameter. The difference of the focal radii of a hyperbola is a constant. It is the distance between the vertices.
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Cheers,
Stan H.
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