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algebra intermediate
Problem
The graph of is the union of the graphs of two different conic sections. Which two types of conic sections are they?
(Write your answer as a list, with "C" for circle, "E" for ellipse, "H" for hyperbola, and "P" for parabola. For example, "C, H" if you think the graph consists of a circle and a hyperbola. You may use a letter twice.)
(Write your answer as a list, with "C" for circle, "E" for ellipse, "H" for hyperbola, and "P" for parabola. For example, "C, H" if you think the graph consists of a circle and a hyperbola. You may use a letter twice.)
Solution
We can rewrite the given equation as The left-hand side is the perfect square of a binomial: Therefore, either or That is, either or These are the equations for a hyperbola and an ellipse, respectively, so the answer is
Final answer
\text{H, E}