Find the standard form of the equation for the circle with the following properties.

Question

Center (9,-7/5) and tangent to the X-axis

Answer 1

The equation has the form (x-9)²+(y+7/5)²=R². The only thing left is to find R. How? Use the property that x-axis is tangent. The center of the circle, point (9, -7/5) is located in the fourth quadrant and since the circle "touches" x-axis, the whole circle is located in the fourth quadrant (below x-axis) and the distance from x-axis to its center, which is radius, R is equal to 7/5. So the equation is

(x-9)²+(y+7/5)²=(7/5)².