Question

Circle A is shown on the coordinates plane shown above

A) write the center and the radius Of the circle
B) write the equation of the circle
C) name three points that lie on the circle
D) find the area of the circle to the nearest square unit

Answer 1

The center of the circle is at (-2, 0). The radius is 5 units. The equation for a circle, in standard form is

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

We have our h and k from the center. h is the x coordinate and k is the y coordinate. The radius is 5. That means that the circle's equation, before simplifying, is

$(x-(-2))^2+(y-0)^2=5^2$. After simplifying it is

$(x+2)^2+y^2=25$. That's A and B. For C, we will simply pick points on the axes. One point on the circle is at (3, 0); another point is at (-2, 5); a third point is at (-7, 0). For D, the area of a circle is

$A=\pi r^2$.

For us that looks like this

$A=\pi (5)^2$. In terms of pi the answer is 25 pi, but in decimal form to the nearest square unit, it's 79 units squared.