Question

The center of a circle is H_10 units below the origin, and the radius is 10 units. What is the equation of this circle?

A. x^2 + (y + 5)^2 = 10
B. (x + 6)^2 + y^2 = 10
C. x^2 + (y + 6)^2 = 100
D. (x + 5)^2 + y^2 = 100

Answer 1

The equation of this circle is
`x^2 + (y + 10)^2 = 100`.

Step-by-step explanation:

The equation of a circle centered at point (h, k) with radius r is given by:

`(x - h)^2 + (y - k)^2 = r^2`

In this case, the center of the circle is at (0, -10) and the radius is 10 units. Substituting the values into the equation, we get:

`(x - 0)^2 + (y - (-10))^2 = 10^2`

Simplifying further, we have:

`x^2 + (y + 10)^2 = 100`

Therefore, the equation of this circle is
`x^2 + (y + 10)^2 = 100`, which corresponds to option C.