# How to ContourPlot a two variables (x,y) implicit function with y normalized?

I am trying to use ContourPlot to plot an implicit function. Now I have two variables (x,y) implicit function:

(b x)/a + y == ((c + d) Log[1 - (n y)/(c + d)])/m


where b/a=0.0065,c+d=-3276.26 and n=9770.6, m=9770.6x{0,60}. I can ContourPlot it y~x correctly. Physically, x is the time, y is the distance.

Actually, the y has the region {0,k}, now I want to ContourPlot it with y normalized, i.e. the x-axis is the time, y-axis is the distance y divided by k (y/k), ranges from 0 to 1. Just like this

• "a,b,c,d,m and n are all known", But I do not know anything about them ? – Mariusz Iwaniuk Sep 27 '18 at 13:38
• I have updated the parameters in the equation. Thank you for your help! – Rick Sep 27 '18 at 13:52
• Using your numbers the expression ((c + d) Log[1 - (n y)/(c + d)])/m results in an imaginary number whenever y is greater than approximately 0.4. One is unable to plot imaginary numbers directly with Plot or ContourPlot – Jack LaVigne Sep 27 '18 at 14:10
• Thank you for your help! – Rick Nov 11 '18 at 4:13

Since the scaling is linear, you can simply relabel the ticks:

k = 3;
ContourPlot[x - y^2, {x, 0, 10}, {y, 0, k},
Contours -> {{1, Red}, {2, Green}, {3, Blue}, {4, Purple}},
FrameTicks -> {{ChartingFindTicks[{0, k}, {0, 1}], Automatic},     Automatic}]

Alternatively, multiply all ys by k in the first argument of ContourPlot and use {y, 0, 1} for the y range:
ContourPlot[x - (k y)^2, {x, 0, 10}, {y, 0, 1},
`