# How do you graph the circle with center at (-4, 2) and radius 5 and label the center and at least four points on the circle, then write the equation of the circle?

##### 1 Answer

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#### Explanation:

You are probably familiar with the fact that a triangle with sides of lengths

That means that all of the following integer points will be on the circle of radius

#(-4, 2) +- (5, 0)" "# i.e.#(-9, 2)# and#(1, 2)#

#(-4, 2) +- (0, 5)" "# i.e.#(-4, -3)# and#(-4, 7)#

#(-4, 2) +- (3, 4)" "# i.e.#(-7, -2)# and#(-1, 6)#

#(-4, 2) +- (4, 3)" "# i.e.#(-8, -1)# and#(0, 5)#

#(-4, 2) +- (3, -4)" "# i.e.#(-7, 2)# and#(-1, -2)#

#(-4, 2) +- (4, -3)" "# i.e.#(-8, 5)# and#(0, -1)#

The equation of a circle with centre

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

So in our case, we can write:

#(x+4)^2+(x-2)^2 = 25#

graph{((x+4)^2+(y-2)^2 - 25)((x+4)^2+(y-2)^2 - 0.04) = 0 [-16.41, 6, -3.64, 7.2]}