Question

How do you find general form of circle centered at (2,3) and tangent to x-axis?

Answer 1

Understand that the contact point with the x-axis gives a vertical line up to the center of the circle, of which the distance is equal to the radius.

`(x-2)^2+(x-3)^2=9`

Explanation:

`(x-h)^2+(x-k)^2=ρ^2`

Tangent to the x-axis means:

• Touching the x-axis, so the distance from the center is the radius.
• Having the distance from it center is equal to the height (y).

Therefore, `ρ=3`

The equation of the circle becomes:

`(x-2)^2+(x-3)^2=3^2`

`(x-2)^2+(x-3)^2=9`