curves in the Cartesian plane defined by quadratic equations in x and y
Conic Sections
two-dimensional curves that are formed when a plane intercepts a double-napped cone
Conic Sections
can be graphed on a coordinate plane
Conic Sections
a pair of congruent, opposite cones connected by a common vertex
Double-napped cone
point of intersection
Vertex
are conic sections that result when the plane that cuts the double-napped cone passes through the vertex
Degenerate conics
General Equation of Conic Sections
Ax2 + Cy2 + Dx + Ey + F = 0
A and B are exactly the same
Circle
A and B are different but have the same sign
Ellipse
A and B have opposite signs
Hyperbola
A = 0 or B = 0 but not both at the same time
Parabola
6x2 + 6y2 + 12x - 24y + 12 = 0
Circle
2x2 + y2 - 4x - 2y - 1 = 0
Ellipse
4x2 - 3y2 - 8x + 24y - 80 = 0
Hyperbola
x2 + 8x - 4y + 36 = 0
Parabola
4x2 - 9y2 - 24x - 72y - 144 = 0
Hyperbola
10y2 - 9x2 - 80 = 0
Hyperbola
20x2 + 40y2 - 800 = 0
Ellipse
x2 + 15y - 27 = 0
Parabola
