Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Tangent to the x axis, a radius of length 2, and abscissa of center is -1 A) x ² + y ² - 2 x - 4 y + 1 = 0 and x ² + y ² - 2 x + 4 y + 1 = 0 B) x ² + y ² + 2 x - 4 y + 1 = 0 C) x ² + y ² + 2 x - 4 y + 1 = 0 and x ² + y ² + 2 x + 4 y + 1 = 0 D) x ² + y ² + 2 x + 4 y + 1 = 0 E) x ² + y ² - 2 x + 4 y + 1 = 0

Question

Quizplus · Accepted Answer

Since the circle is tangent to the x-axis and has a radius of length 2, we know that the center of the circle lies on the line x=-1 and is 2 units away from the x-axis. This means that the y-coordinate of the center is -2. 
So the center of the circle is (-1,-2) and the equation of the circle can be written in the form:
(x+1)^2 + (y+2)^2 = 4 
Expanding this equation and rearranging, we get:
x^2 + y^2 + 2x + 4y + 1 = 0

So, the correct answer is option C, which includes this equation as one of its choices.

Find the Equation of the Circle That Satisfies the Following