Conic sections can each be descnbed as the intersection of a

Conic sections can each be descnbed as the intersection of a plane and a double-napped cone. On the diagram of a double-napped cone below, draw a dashed line to indicate where a plane would slice throuhg the cone in order to form the conics given. Be sure to label your lines with the type of conic they are forming. Use the definition of a parabola and the distance formula to derive the standard equation of a parabola which has the origin for its verted, the x-axis as the axis of symmetry, a focus of (p,0), and adirectrix = P.

Solution

(15)

The equation of the parabola with vertex at (0,0) with x axis as the line of symmetry and x=-p as the directrix and (p,0) as the focus is given as

(y-0)² = 4p(x-0)

i.e. y² = 4px