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Identifying Ellipses,Circles and Parobolas w/Picture

*How can you tell if its an ellipse, circle or a parobola? *

I noticed that the Parobla only has one term with a degree of 2 .

I noticed that the circle has same coefficients with their terms like y=x^2 +y^2 another example of cirlce y=9x^2 +9x^2

The Ellipse has different number coefficents that are not the same value like this. 4x^2 +5y^2

Does this sound about right? Im just seeing whats the difference so when the test question comes about identifying I will be equipped and not decieved.

Re: Identifying Ellipses,Circles and Parobolas w/Picture

Do you know the general formulas of each? If you do, then there should be no trouble. Parabolas are very easy to see, but the difference between circles and ellipses are elusive. Think of a circle as an ellipse where the major and minor axis lengths are the same. That way, justturn the equation into an ellipse and if they are the same, it is a circle, if not it is an ellipse. From the sheet, you are correct for all problems.

Re: Identifying Ellipses,Circles and Parobolas w/Picture

A quadratic equation in two variables will be a circle if the coefficient of x^2 is equal to coefficient of y^2and coefficient of xy is 0.

A quadratic equation in two variables will be a Parabola if the coefficient of x^2 or coefficient of y^2 is 0 and coefficient of xy is 0.

E an eclipse else a hyperbola.

A quadratic equation in two variables will be an Ellipse or Hyperbola if the coefficient of x^2 is not equal to coefficient of y^2and coefficient of xy is 0. If the sign of both x^2 and y^2 is same it will be an ellipse else a hyperbola

Re: Identifying Ellipses,Circles and Parobolas w/Picture

Thanks for all the extra help and I don know the stand forms for all of them by hard.