Question

A circle has radius 10 unites and passes through the point (5;-16). the x-axis is a tangent to the circle. find the possible equations of the circle.

A) x²+(y+10)²=10²
B) x²+(y−10)²=10²
C) x²+(y+6)²=10²
D) x²+(y−6)²=10²

Answer 1

To find the equation of the circle, we need the coordinates of the center and the radius. The circle has a center at (5,10) and a radius of 10 units. Therefore, the possible equation of the circle is x²+(y+10)²=10².

Step-by-step explanation:

To find the equation of a circle, we need the coordinates of the center and the radius. In this case, the circle has a radius of 10 units and passes through the point (5,-16).

Since the x-axis is a tangent to the circle, the center of the circle is at (5,10) and the radius is 10 units.

The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2.

Substituting the values, we get (x-5)^2 + (y-10)^2 = 10^2. Simplifying further, we get the equation x^2 + (y-10)^2 = 100.

Therefore, the possible equation of the circle is A) x²+(y+10)²=10².