The geometric shapes obtained by slicing a double-napped cone Conic Sections The geometric shapes obtained by slicing a double-napped cone A cone is formed when two lines meet at an acute angle and one of the lines is rotated around the other

Circle

Ellipse

Parabola

Hyperbola

Ellipse The set of all points (x,y) the sum of whose distances from two distinct fixed points(foci) is constant

MINOR AXIS CENTER (h,k) MAJOR AXIS Vertex

(x-h)^2 + (y-k)^2 = 1 a^2 b^2 Standard Equation of an Ellipse (h,k) is the center of the circle a is ½ of the major axis b is ½ of the minor axis

Eccentricity e = c/a c^2 = a^2 – b^2 Measures the ovalness of an ellipse e = c/a If c/a is small the ellipse is circular If c/a is close to 1 then the ellipse is elongated c^2 = a^2 – b^2