So my Professor ask us to solve a problem finding the equation of the circle with only a given
"Tangent to the x-axis with center on x + 4y = 5"
I'm confused in the part how do I find the center point in a line without a given endpoints of the line?
What I think about the problem is that the center would be along the given line and the x intercept would be the point where the circle touches
Edit: after analyzing how it could be done. I found out that it really isn't a unique circle, the center and the x axis can be adjusted to match the given.
This is the first graph of equation
This is another one that was adjusted
My problem now is how do I create an differential equation of family of circles that would only satisfy the given problem.
Sorry I'm new, thank you for everyone's kind response
There are obviously not a unique one but multiple ( an infinite set) circle solutions.
They can be set by a variable center point given on the given parametrized straight line
$$ (x_C,y_C)=(t, \frac{5-t}{4})$$
You can find them all
$$ (x-x_C)^2+(y-y_C)^2= y_C^2.$$
Find the equation of Circle in the question misleads.