What are Conic Sections? By Kelsey Lumsden

What is a conic section? A curve contained by the intersection of a cone with a plane Four types of conic sections are… Parabola Ellipse Circle Hyperbola

Parabola A conic section created by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Can also be written as to allow the vertex to be at a different point (h,k) other than the origin.

Ellipse Is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve.

The line segment that goes through the foci and connects to the vertices, is called the major axis. The line segment that is perpendicular to the major axis and passes through the midpoint is called the minor axis. It connects the co vertices. Vertex (0,b) Focus (0,C) Equation Major axis Vertices Co vertices x^2 + y^2 =1 Horizontal (+/-a,0) (0, +/-b) a^2 b^2 x^2 + y^2 =1 Vertical (0, +/-a) (+/-b,0) b^2 a^2 Co Vertex (-a,0) Co Vertex (a,0) Focus (0,-C) Co Vertex (0,b) Focus (-C,0) Focus (C,0) Vertex (a,0) Vertex (-a,0) Vertex (0,-b) Co Vertex (0,-b) The foci of the ellipse lie on the major axis, C units from the center. C^2 = a^2 – b^2

Circle A conic section attained when a right circular cone is intersected by a plane perpendicular to the axis of the cone. X^2 + y^2 = r^2 r

Hyperbola Made of two parabolas, reflected over a line