# A circle has a center that falls on the line #y = 5/3x +1 # and passes through #(8 ,2 )# and #(3 ,1 )#. What is the equation of the circle?

The equation of the circle is

Two equations are available.

So,

The circle's radius is

The circle's equation is

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To find the equation of the circle, follow these steps:

- Determine the center of the circle.
- Use the distance formula to find the radius of the circle.
- Use the center and radius to write the equation of the circle in standard form.

Given:

- The center of the circle lies on the line ( y = \frac{5}{3}x + 1 ).
- The circle passes through the points (8, 2) and (3, 1).

Step 1: Since the center of the circle lies on the line ( y = \frac{5}{3}x + 1 ), let's denote the coordinates of the center as ((x_0, y_0)). Substitute (y = \frac{5}{3}x + 1) into the coordinates of the center to find (x_0) and (y_0).

Step 2: Use the center and one of the given points to find the radius of the circle using the distance formula:

[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

Step 3: Write the equation of the circle in standard form, which is ((x - x_0)^2 + (y - y_0)^2 = r^2), where ((x_0, y_0)) is the center of the circle and (r) is the radius.

Follow these steps to find the equation of the circle. If you need further clarification on any step, feel free to ask!

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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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