Question

The center of a circle is at (-2,-7) and its radius is 6. What is the equation of the circle?

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Answer 1

Answer: (x+2)^2+(y+7)^2=36

Explanation:

To write an equation for a circle when you know

the radius is R

the center is at (A, B), remember that the standard form of the equation of the circle is:

Just plug those values into this equation:

(x-A)^2+(y-B)^2=R^2

You will end up with this equation

(x+2)^2+(y+7)^2=36

Answer 2

(X+2)^2 +(Y+7)^2 =36

Since the centre of the circle is (-2;-7), we equate the variable to its coordinate:

X=-2

Y=-7

now we bring the coordinate over to the left side which changes its sign.

X+2=0

Y+7=0

That explains the :

(X+2)^2 +(Y+7)^2

Now for the R.

its given that the radius is 6 and since the standard form for the equation of a circle requires r^2.

we simply square 6.

6^2=36.