SOLUTION: Write the standard equation of an ellipse with the first focus being (-4,0) and the second one being (4,0), passing through (4,1)

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Question 1119425: Write the standard equation of an ellipse with the first focus being (-4,0) and the second one being (4,0), passing through (4,1)
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


With foci at (-4,0) and (4,0), the center of the ellipse is at (0,0). The equation is of the form



The distance from the center of the ellipse to each focus is c, where

Since that distance is 4, we have




Then the equation of the ellipse can be written as



We can find the value of b^2 by plugging in the coordinates of the known point on the ellipse, (4,1).







Then



And finally the equation is


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