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Given the choices below fill in the correct expression in each box to create the equation of the given circle Circles

Given the choices below fill in the correct expression in each box to create the equation-example-1
User FLBKernel
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1 Answer

13 votes
13 votes

Given a diameter LM and its coordinates.

The coordinate of the center is the midpoint of LM

Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Coordinate of the center = [(-4+12)/2, (-8+4)/2]

Coordinate of the center = (4, -2)

Now to get the length of the radius, get the distance of LM and divide it by 2 :


d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}
d=\sqrt[]{(4+8)^2+(12+4)^2}

d = 20

and the radius is 20/2 = 10

Now we have the center at (4, -2) and a radius of 10

The standard equation of a circle is :

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

where h and k are the center of the circle (h, k)

So the equation will be :

(x-4)^2 + (y+2)^2 = 10^2

or

(x-4)^2 + (y+2)^2 = 100

User Andy Clarke
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