How do you determine which conic section an equation describes?
In the form Ax^2+Cy^2+Dx+Ey+F the rule is simply: if A=C it is a circle if A and C have the same sign (+) or (-) it is an ellispe if A and C have oppsite signs, one positive one negative it is a hyperbola if A or C (but not both) equal zero it is a parabola However is there is an ‘xy’ term in the conic and it is of the form: Ax^2+Bxy+Cy^2+Dx+Ey+F then the rule is you take B^2-4AC and if that value is: <0 it is an ellipse >0 it is a hyperbola =0 it is a parabola (a circle will never have an xy term)
