Question

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

Answer 1

(x − 5)² + (y − 4)² = 4²

(x − 5)² + (y + 4)² = 4²

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

Answer 2

Explanation:

Given that a circle has tangents x=1, x=9 and y=0

Since two parallel lines are tangents the distance between these two lines give diameter of the circle

Distance between x=1 and x=9 is
`9-1 =8` units

radius = 4 units ...i

Since y=0 is tangent, the centre will be having y coordinate as 4.

Since centre lies in the middle of x=1 and x=9 the centre will have x coordinate

as 5

Hence equation of the circle is

`(x-5)^2+(y-4)^2 = 16`