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What conic is $x^2 - y^2 - 2y - 2=0$ and what is the conic format of it? It would be great if work was shown so I could learn it. I know it's either a hyperbola or an eclipse but I don't know how to convert it to one

Ojas
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SocketPhys
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  • think of the equation as a quadratic in $y$ with $a = 1, b = 2, c = 2-x^2.$ solve for $y.$ plot them and see what it looks like. – abel May 29 '15 at 05:21

2 Answers2

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$x^2 -(y+1)^2 = 1$, canyou tell what it is?

DeepSea
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  • Got it. It's a hyperbola right? I kept trying to complete the square with x^2 also so I never got it. Thank you! – SocketPhys May 29 '15 at 05:20
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Hint

When you are so lucky that the equation does not contain the unpleasant $x\times y$ term and is written $$Ax^2+By^2+Cx+Dy+E=0$$ just complete the squares to get $$A\Big(x+\frac C{2A}\Big)^2+B\Big(y+\frac D{2B}\Big)^2+\Big(E-\frac{C^2}{4 A}-\frac{D^2}{4 B}\Big)=0$$ and you easily see what the conic is : if $AB>0$ it is an ellipse ( if moreover $A=B$ it is a circle), if $AB<0$ it is an hyperbola, if $AB=0$ it is a parabola.

Claude Leibovici
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