Given the standard equation of a circle:
x^2 + y^2 + 7x - 2y + 6 = 0 --Simplified-to--> (x+7/2)^2 + (y-1)^2 = 29/4
Standard formula of a circle: (x + (-h))^2 + (y + (-k))^2 = r^2 The center is represented by (h, k); radius by sqrt(r^2).
So my first question is, is there are way I could insert either of the 1st 2 equations and have Sage 5.9 generate the circle?
My second question similarly deals with an ellipse that has the simplified equation:
((x+2)^2)/9 + ((y-1)^2)/25 = 1
Its major axis is: (-2,-4) (-2,6) Minor axis is: (-5,1) (1,1)
Standard form of an ellipse is: ((x - (-h))^2)/b^2 + ((y + (-k))^2)/a^2
Center is determined by analyzing the differences between the x2/x1, y2/y1 coordinates of the major or minor axis (i.e. midpoint formula).
Could I generate an ellipse baed on the simplified equation?
In case anyone's interested, the following thread has an unanswered question: http://ask.sagemath.org/question/2764/graph-based-on-y-value-as-the-input-and-x-as-the
