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

1 Answer
Jan 14, 2016

Answer:

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#