For a circle two diameter are `x+y=3, x-y=1` then centre is

Options

A. (-1,4)
B. (3,0)
C. (1,2)
D. (2,1)

Answer

To find the center of the circle given two diameters represented by the equations \(x + y = 3\) and \(x - y = 1\), we can follow these steps:

### Step 1: Write down the equations of the diameters
The two diameters are given as:
1. \(x + y = 3\) (Equation 1)
2. \(x - y = 1\) (Equation 2)

### Step 2: Add the two equations
To find the x-coordinate of the center, we can add both equations:
\[ (x + y) + (x - y) = 3 + 1 \]
This simplifies to:
\[ 2x = 4 \]

### Step 3: Solve for x
Now, divide both sides by 2:
\[ x = \frac{4}{2} = 2 \]

### Step 4: Substitute x back into one of the equations to find y
We can substitute \(x = 2\) back into Equation 1:
\[ 2 + y = 3 \]
Now, solve for \(y\):
\[ y = 3 - 2 = 1 \]

### Step 5: Write the center of the circle
The center of the circle is given by the coordinates \((x, y)\):
\[ \text{Center} = (2, 1) \]

### Final Answer
The center of the circle is \((2, 1)\).

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