35-46 Finding the Equation of a Shifted Conic Find an equation for the conic section with the given properties.
The ellipse with foci and that passes through the point .
The equation of a shifted conic for ellipse with foci and that passes through the point .
Shifting graph of equations
If h and k are real numbers, then replacing by or by and replacing by or by .
The foci and is lie on the vertical axis, so equation has the form,
Replace by , and by .
The center is midway of the foci so the coordinates of the center will be as follows,
Substitute for , for , for , and for in the above center formula.
Compare the coordinate of foci with . So,
The ellipse passes through the point , point , and must lie on ellipse.
Substitute for , for , for , and for in equation
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