# SOLUTION: How do you know the difference if a a question is whether a circle or an ellipse? for an example.. 7x^2 + 7y^2 - 10x + 14y - 20 = 0 i know that when its a parabola, neithe

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 Algebra: Conic sections - ellipse, parabola, hyperbola Solvers Lessons Answers archive Quiz In Depth

 Question 447769: How do you know the difference if a a question is whether a circle or an ellipse? for an example.. 7x^2 + 7y^2 - 10x + 14y - 20 = 0 i know that when its a parabola, neither A nor C is zero, and A and C have the same sign, which its not an hyperbola.Answer by lwsshak3(6505)   (Show Source): You can put this solution on YOUR website!How do you know the difference if a a question is whether a circle or an ellipse? for an example.. 7x^2 + 7y^2 - 10x + 14y - 20 = 0 .. To determine whether given equation or any equation is a circle or an ellipse, you must see the equation in standard form. To do this, you may need to complete the square For an ellipse: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b) (horizontal major axis) or (x-h)^2/b^2+(y-k)^2/a^2=1 (a>b) (vertical major axis) For a circle: (x-h)^2+(y-k)^2=r^2 let us complete the square for given equation 7x^2 + 7y^2 - 10x + 14y - 20 = 0 7(x^2-10/7x+(10/14)^2)+7(y^2+2y+1)=20+7*(10/14)^2)+7 7(x-10/14)^2)+7(y+1)^2=20+7*(10/14)^2)+7 Without going thru with all the arithmetic, you can see this will become an ellipse by dividing every term by the right side of the equation. The equation of a circle looks looks like that of an ellipse except the denominators of the x^2 and y^2 terms can be made to be 1 and the right side radius does not have to be 1 like an ellipse. Hope this helps!