More on the line tangent to a circle

Some may be confused when the derivative of the constant in the equation goes to zero.

You may ask; what happens when the number is something else, say 42 rather than 25. The circle is certainly different. It has a radius of ~6.5 now, not 5. Isn't this going to make a difference? How could both of the slopes be the same?

A circle with a different radius gives the same slope equation. What's up!?

Well, the slope equations are the same, but the slopes are NOT because, although x is the same for both problems ( x = 3 ), the y's are going to be different (remember, you substitute x into the original equation to find y before you substitute into the slope equation).

Below is a Graph Theory showing both circles and the two tangent lines using the same slope equation. The black line just shows you where x = 3 is. It is obvious that the slopes are not the same.