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haleyking345
Is this a parabola, hyperbola, ellipse, or circle? a.) y^2 + 2x^2 - 10 = 0
Do you remember what the `standard form` for each parabola, hyperbola, ellipse and circle look like? :) We'll want to take this function and put it into one of those standard forms so we can easily identify which one it is.
\[\large y^2+2x^2-10 = 0\]Adding 10 to both sides gives us,\[\large y^2+2x^2=10\]Divide both sides by 2,\[\large \frac{y^2}{2}+x^2=5\] Hmm let's write it like this, and see if it looks familiar.\[\large \frac{y^2}{2}+\frac{x^2}{1}=5\]
Ah yes it is! I should have gone one more step to make the right side 1, my mistake.\[\large \frac{y^2}{10}+\frac{x^2}{5}=1\] But yes, very good, ellipse. :)