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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(11628)   (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!
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