# A circle has a center that falls on the line #y = 1/7x +4 # and passes through # ( 5 ,8 )# and #(5 ,6 )#. What is the equation of the circle?

The equation of the circle is

the circle.

The circle's radius is

The circle's equation is

graph{[-26.26, 46.76, -9.13, 27.44]} = (x-21)^2+(y-7)^2-257)(y-x/7-4)(y-7)=0

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To find the equation of the circle, we need to determine its center and radius. The center of the circle lies on the line y = (1/7)x + 4. Since both points (5, 8) and (5, 6) lie on this line, the x-coordinate of the center is 5.

To find the y-coordinate of the center, substitute x = 5 into the equation of the line: y = (1/7)(5) + 4 y = 5/7 + 4 y = 5/7 + 28/7 y = 33/7

So, the center of the circle is (5, 33/7).

Now, we can find the radius of the circle using one of the given points, let's say (5, 8): r = sqrt((x - h)^2 + (y - k)^2) r = sqrt((5 - 5)^2 + (8 - 33/7)^2) r = sqrt((0)^2 + (56/7 - 33/7)^2) r = sqrt(0 + (23/7)^2) r = sqrt(529/49) r = 23/7

Now, we have the center (h, k) = (5, 33/7) and the radius r = 23/7.

The equation of a circle is given by (x - h)^2 + (y - k)^2 = r^2. Substituting the values, we get: (x - 5)^2 + (y - 33/7)^2 = (23/7)^2

Thus, the equation of the circle is (x - 5)^2 + (y - 33/7)^2 = 529/49.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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