Question

Which conic section is represented by the following equation?
5x^2 - x + 5y^2 - 3y - 12 =0

Answer 1

Ax²+Bx+Cy²+Dy+E=0

so in the template above for a conic, the defining components are the coefficients A and C

• If either A=0 or C=0, then the equation is a Parabola

• if A=C, then we have a Circle

• if either A or C is negative, and A≠C, then we have a Hyperbola

• if A and C are both positive or both negative, and A≠C, then we have an Ellipse.

notice, 5x² and 5y² have the same coefficient, thus a circle baby!