Question

Which of the following equations will produce this graph? (Please help @sqdancefan)

Answer 1

The correct answer is B. (x-3)^2+(y-7)^2=16.

I used a graphing calculator to find this answer, but the way to do it without a calculator is to plug each set of coordinates in the circle into each equation to solve. In example, if I plugged the coordinates (7,7) into the correct equation:

(7-3)^2+(7-7)^2=16

4^2+0^2=16

16+0=16

16=16

As you can see, it shows that the coordinates work.

I hope this helps :)

Answer 2

The equation of a circle:

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

(h, k) - center

r - radius

We have the points A(-1, 7) and B(7, 7). AB is a diameter of a circle.

The midpoint of diameter is a center of a circle.

Calculate this using:

`M\left((x_1+x_2)/(2),\ (y_1+y_2)/(2)`

Substitute

`M\left((-1+7)/(2),\ (7+7)/(2)\right)\to M(3,\ 7)`

Therefore we have h = 3 and k = 7.

Calculate a length of a radius using:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Substitute coordinates of the points (3, 7) and (7, 7):

`r=√((7-3)^2+(7-7)^2)=√(4^2)=4`

Your answer is:

`(x-3)^2+(y-7)^2=4^2\\\\\boxed{(x-3)^2+(y-7)^2=16}`

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You can read the coordinates of the center and length of a radius from a graph.

Look at the picture.