Find an equation of the circle tangent to the lines x=1, x=9, y=0

(x − 5)² + (y − 4)² = 4²

(x − 5)² + (y + 4)² = 4²

Step-by-step explanation:

x=1 and x=9 are vertical lines.  If both are tangent to the circle, then the circle has a diameter of 8, or a radius of 4, and the center of the circle is on the line x=5.

y=0 is the x-axis.  Since the circle is tangent to that, the center of the circle is either 4 units above the x-axis or 4 units below.

So two possible equations of the circle are:

(x − 5)² + (y − 4)² = 4²

(x − 5)² + (y + 4)² = 4²

Here's a graph: desmos.com/calculator/9e4lxx731u

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