If the equation `4x^2+hxy+y^2=0` represent coincident lines, then h is equal to

Options

A. 1
B. 3
C. 2
D. 4

Explanation

To find the value of \( h \) such that the equation \( 4x^2 + hxy + y^2 = 0 \) represents coincident lines, we can follow these steps:

### Step 1: Identify the coefficients
The given equation can be written in the standard form of a quadratic in \( x \) and \( y \):
\[ Ax^2 + Bxy + Cy^2 = 0 \]
Here, we have:
- \( A = 4 \)
- \( B = h \)
- \( C = 1 \)

### Step 2: Use the condition for coincident lines
For the equation to represent coincident lines, the condition is given by:
\[ B^2 - 4AC = 0 \]
This means the discriminant of the quadratic must be zero.

### Step 3: Substitute the values of A, B, and C
Substituting the values we identified:
\[ h^2 - 4(4)(1) = 0 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ h^2 - 16 = 0 \]

### Step 5: Solve for \( h \)
To find \( h \), we can rearrange the equation:
\[ h^2 = 16 \]
Taking the square root of both sides gives us:
\[ h = \pm 4 \]

### Conclusion
Thus, the values of \( h \) for which the equation represents coincident lines are:
\[ h = 4 \quad \text{or} \quad h = -4 \]

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