Answer:
k = -8c.
Step-by-step explanation:
y^2 = kx
Find the slope of the tangent by differentiating:
y' 2y = k
y' = k / 2y = the slope of the tangent.
The given equation of the tangent is y = -2x + c so the slope = -2.
Therefore k/2y = -2 so k = -4y and y = -k/4
y^2 = kx so k^2/16 = kx giving x = k/16.
Substituting for x and y in y = -2x + c:
-k/4 = -2 k/16 + c
-k/4 = -k/8 + c
c = -k/4 + k/8 = -k/8.
So -k = 8c
k = -8c.
