SOLUTION: Find the equation of an ellipse that passes through A(3,5) and B(7,5/3) whose axis coincides with the coordinate axis.

Question 1130622: Find the equation of an ellipse that passes through A(3,5) and B(7,5/3) whose axis coincides with the coordinate axis.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

An ellipse has two axes; and there are two coordinate axes. So when the statement of the problem sloppily says "the" axis of the ellipse coincides with "the" coordinate axis, I will assume that the intended meaning is that both axes of the ellipse coincide with both coordinate axes -- i.e., the center of the ellipse is at the origin.

Then the equation of the ellipse is

Form two equations in a^2 and b^2 using the two known points on the ellipse and solve the pair of equations to find the equation of the ellipse.

Multiply the second equation by 9 and subtract one equation from the other to eliminate b:

Substitute in either original equation to find b^2:

We nowknow a^2 and b^2 for the ellipse, so we can write its equation:

ANSWER:
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