■ Finding the Equation of a Shifted Conic Find an equation for the conic whose graph is shown.
The equation of the conic.
The graph of the conic section is given below.
For an equation in and , if the value of is replaced by , then the graph is shifted horizontally and if the value of is replaced by , then the graph is shifted vertically.
The equation of an ellipse centred at is given by the following formula.
Consider the graph of the conic.
The major axis is the vertical axis.
The coordinates of the major axis are and .
The center of the ellipse is the midpoint of the major axis.
Therefore, the center of the ellipse is given below.
The length of the major axis is given below.
Therefore, the value is given below.
The coordinates of the minor axis are and
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