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
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]}