Question

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

Answer 1

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