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
George C.
Aug 10, 2018

See explanation...

Explanation:

You are probably familiar with the fact that a triangle with sides of lengths #3#, #4# and #5# is a right angled triangle.

That means that all of the following integer points will be on the circle of radius #5# with centre #(-4, 2)#:

#(-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 #(h, k)# and radius #r# can be written:

#(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]}

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