Properties Of Conic Sections

M1 y x c m2 y x c and by implicit differentiation m3 x y.

Properties of conic sections. This value is constant for any conic section and can define the conic section as well. M2 the slope of the line from p to f2 and m3 the slope of the tangent line. 9 6 properties of the conic sections contemporary calculus 2.

Depending on the angle of the plane relative to the cone the intersection is a circle an ellipse a hyperbola or a parabola. A conic section can be graphed on a coordinate plane. A cos θ b sin θ parabola.

If e 1 e 1 it is an ellipse. Conic sections are mathematically defined as the curves formed by the locus of a point which moves a plant such that its distance from a fixed point is always in a constant ratio to its perpendicular distance from the fixed line. B 2 a 2.

1 m slope of1p m slope of2f2p m slope of tangent line at p. Standard forms in cartesian coordinates. A conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane.

D t d t displaystyle dt frac d t where d c 2. At 2 2 at hyperbola. If e 1 e 1 the conic is a parabola.

A sec θ b tan θ or a cosh u b sinh u rectangular hyperbola. The three types are parabolas ellipses and hyperbolas. The three types of curves sections are ellipse parabola and hyperbola.