Mathematics

Problem

For the parabola

x^{2}=20y

, let

R

be a point on the curve with ordinate

k^{2}

, where

k>0

. a. (i) Determine the abscissa(s) of

R

in terms of

k

. b. (ii) Obtain a formula for the distance of

R

from the focus of the parabola, expressed in terms of

k

. c. (iii) If this distance equals

13

, find the corresponding value(s) of

k