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

Jan 14, 2016

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.

${\left(x - 2\right)}^{2} + {\left(x - 3\right)}^{2} = 9$

#### 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:

${\left(x - 2\right)}^{2} + {\left(x - 3\right)}^{2} = {3}^{2}$

${\left(x - 2\right)}^{2} + {\left(x - 3\right)}^{2} = 9$