Mathematics

Problem

The curve

C

is given by

x=kt+1

and

y=t^{2}-3t

, where

k

is a real constant. a. (i) The tangent to

C

at the point corresponding to

t=2

passes through the fixed point

(5,-2)

. Determine the value of

k

. b. (ii) Using the value of

k

found in part (i), obtain the equation of the tangent to

C

t=2

. c. (iii) Express the equation from part (ii) in slope–intercept form

y=mx+c

and state the slope of the tangent explicitly.