The equation of the circle with centre at `(1, 3)` and radius 3 is

Options

A. `(x-1)^(2) + (y-3)^(2) = 9`
B. `(x+1)^(2) + (y+3)^(2) = (3)^(2)`
C. `(x-3)+(y-1)^(2) = 3`
D. `(x+3)^(2) + (y+1)^(2) = (3)^(2)`

Answer

To find the equation of the circle with center at (1, 3) and radius 3, we can follow these steps:

### Step 1: Identify the center and radius
The center of the circle is given as (1, 3), which means:
- \( a = 1 \)
- \( b = 3 \)

The radius of the circle is given as 3, which means:
- \( r = 3 \)

### Step 2: Use the standard form of the equation of a circle
The standard form of the equation of a circle with center \((a, b)\) and radius \(r\) is:
\[ (x - a)^2 + (y - b)^2 = r^2 \]

### Step 3: Substitute the values into the equation
Now, substituting the values of \(a\), \(b\), and \(r\) into the standard form:
\[ (x - 1)^2 + (y - 3)^2 = 3^2 \]

### Step 4: Simplify the equation
Calculating \(3^2\):
\[ 3^2 = 9 \]
So the equation becomes:
\[ (x - 1)^2 + (y - 3)^2 = 9 \]

### Final Equation
Thus, the equation of the circle with center at (1, 3) and radius 3 is:
\[ (x - 1)^2 + (y - 3)^2 = 9 \]

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