Sect' 8'6 Conic Sections

1
Sect. 8.6 Conic Sections
Goal 1 Write equations of Conic Sections
in Standard Form Goal 2 Identify Conic
Sections from their Equations
2
Here are all of the conic sections
Circle
Parabola
Hyperbola
Ellipse
3
In the following equations the point (h, k) is
the vertex of the parabola and the center of the
other conics.
(x h) 2 (y k) 2 r 2
CIRCLE
4
General Form of a Quadratic Equation
Ax2 Bxy Cy2 Dx Ey F 0
Identifying Conic Sections
Circle
A C
A and C have the same sign, but A ? C
Ellipse
A and C have opposite signs
Hyperbola
5
Identify whether each equation is a Parabola,
Circle, Ellipse or Hyperbola.
1) 3y2 x2 9 0
Hyperbola
2) 2x2 2y2 16x 20y - 32
Circle
3) y2 2x 4y 10 0
Parabola
Ellipse
4) x2 4y2 2x 24y 33 0
Ellipse
5) 3x2 2y2 12x 24y 104 0
Hyperbola
6) 4x2 10x 34y 21 4y2
7) 0.04x2 x y 3 0
Parabola