Want help in part 2?
1 Answer
Explanation:
Normal means perpendicular to the curve. The given normal line can be rewritten as follows:
#y = 1/2x + c/2#
This means that the slope is
Thus we must find the values of
#y = 4(2x - 1)^-1#
The derivative as given by the chain rule is
#y' = -8/(2x- 1)^2#
Set
#-2 = -8(2x- 1)^2#
#1/4 = (2x- 1)^2#
#+- 1/2 = 2x - 1#
#2x= 3/2 and 2x = 1/2#
#x = 3/4 and x = 1/4#
The curve's corresponding y-values are given by calculating using the function
#y(3/4) = 4/(2(3/4) - 1) = 4/(1/2) = 8#
#y(1/4) = 4/(2(1/4) - 1) = 4/(-1/2) = -8#
We now solve for
#2(8) = 3/4 + c -> c= 16 - 3/4 -> c = 61/4#
#2(-8) = 1/4 + c-> c = -16 - 1/4 -> c = -65/4#
Hopefully this helps!