Consider the parabola whose axis is the -axis

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Consider the parabola

x^{2}=16y

whose axis is the

y

-axis. A point

Q(4,9)

is taken in the plane. (i) Find the coordinates of the point

Q'

that is the reflection of

Q

in the axis of the parabola. (ii) Determine the coordinates of the midpoint

M

of the segment

QQ'

. (iii) Show that the midpoint

M

obtained in part (ii) lies on the axis of the parabola and calculate its distance from the vertex.