43-54 ■ Indentifying and Graphic a conic Determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is ellipse, find the center foci and vertices. If it is parabola, find the vertex, focus, and directrix. If it is hyperbola, find the center, foci, vertices and asymptotes. Then sketch the graph of the equation. If the equation has no graph, explain why.
Whether the equation represents an ellipse, a parabola, or a hyperbola. If the graph is an ellipse, find the center, foci, and vertices. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Sketch the graph of the equation. Mention the reason, if equation has no graph.
Rearrange the terms into the equation of conic and compare the equation with the standard equations of conics.
Rearrange the terms, as follows
Above equation is an equation of an ellipse. Compare the above equation with the standard equation of the shifted ellipse .
Center of the ellipse will be . Since and , then and
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