Mathematics, 09.12.2020 07:50 rutza
Derive the equation of the ellipse with foci at (1,0) and (−1,0) whose distance between vertices is 6.
Make a picture to help. Label the foci, and place and label a point (x, y) along the ellipse. Draw the focal distances from the point (x, y) to each focus point.
Hint: Note that the endpoints on the major axis are often called vertices (the other endpoints on the minor axis are called co-vertices).
Use the fact that the distance between the vertices is equal to the sum of the focal distances. Use the distance formula to start.
Put the steps in order:
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Derive the equation of the ellipse with foci at (1,0) and (−1,0) whose distance between vertices is...
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