If (8, 2) is a solution of `x+4y-2k=0` then find the value of `k^2`.

Options

A. 36
B. 49
C. 64
D. 81

Answer

To solve the problem, we need to find the value of \( k^2 \) given that the point \( (8, 2) \) is a solution to the equation \( x + 4y - 2k = 0 \).

### Step-by-Step Solution:

1. **Substitute the values of \( x \) and \( y \)**:
Since \( (8, 2) \) is a solution, we substitute \( x = 8 \) and \( y = 2 \) into the equation:
\[ 8 + 4(2) - 2k = 0 \]

2. **Calculate \( 4(2) \)**:
Calculate the term \( 4 \times 2 \):
\[ 4(2) = 8 \]

3. **Rewrite the equation**:
Substitute \( 8 \) back into the equation:
\[ 8 + 8 - 2k = 0 \]

4. **Combine like terms**:
Combine the constants:
\[ 16 - 2k = 0 \]

5. **Isolate \( k \)**:
Rearranging the equation to solve for \( k \):
\[ 2k = 16 \]
\[ k = \frac{16}{2} = 8 \]

6. **Calculate \( k^2 \)**:
Now, we find \( k^2 \):
\[ k^2 = 8^2 = 64 \]

### Final Answer:
Thus, the value of \( k^2 \) is \( 64 \).

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