# A circle has a center that falls on the line #y = 1/7x +4 # and passes through # ( 7 ,8 )# and #(3 ,6 )#. What is the equation of the circle?

The equation of a circle is given by:

So the equation of the circle is:

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The equation of a circle with center ((h, k)) and radius (r) is given by ((x - h)^2 + (y - k)^2 = r^2).

First, we need to find the center of the circle. Since the center lies on the line (y = \frac{1}{7}x + 4), we can substitute this equation into the general form of the circle equation to find the center. So, we have:

((x - h)^2 + (\frac{1}{7}x + 4 - k)^2 = r^2).

Next, we use the fact that the circle passes through the points ((7, 8)) and ((3, 6)). Plugging these points into the circle equation, we get two equations:

((7 - h)^2 + (\frac{1}{7} \cdot 7 + 4 - k)^2 = r^2), and

((3 - h)^2 + (\frac{1}{7} \cdot 3 + 4 - k)^2 = r^2).

Now, we have a system of three equations with three unknowns ((h), (k), and (r^2)). Solving this system will give us the values of (h), (k), and (r^2), which we can then use to write the equation of the circle.

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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.

- A triangle has corners at #(4 ,3 )#, #(1 ,9 )#, and #(6 ,3 )#. What is the radius of the triangle's inscribed circle?
- Two circles have the following equations #(x -2 )^2+(y -4 )^2= 36 # and #(x +8 )^2+(y +3 )^2= 49 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- A triangle has corners at #(2 , 6 )#, #(4 ,7 )#, and #(1 ,5 )#. What is the radius of the triangle's inscribed circle?
- A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 7 ,3 )# and #(5 ,1 )#. What is the equation of the circle?
- A triangle has corners at #(3 ,8 )#, #(7 ,9 )#, and #(4 ,6 )#. What is the area of the triangle's circumscribed circle?

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