SOLUTION: Write the equation of the ellipse that has a center at (5,-4), a vertex at (12,-4), and a covertex at (5,-6).

Question 1204200: Write the equation of the ellipse that has a center at (5,-4), a vertex at (12,-4), and a covertex at (5,-6).
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52868) (Show Source): You can put this solution on YOUR website!
.

The center is given - hence, all you need is to find semi-axes.

Find them from the given information.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The standard form of the equation of an ellipse with center
(, ) and major axis parallel to the -axis is

where

the length of the major axis is
the coordinates of the vertices are (±, )
the length of the minor axis is
the coordinates of the co-vertices are (, ±)
the coordinates of the foci are ( ± , ), where
the ellipse that has
a center at (,)

Thus, ,
vertex at (,)=> ( ± ,)=>

a covertex at (,)=>(,±)

your ellipse is

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