Consider a pair of perpendicular straight lines `ax^(2)+3xy-2y^(2)-5x+5y+c=0`.
The value of a is

Options

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

Explanation

To find the value of \( a \) in the equation of the pair of perpendicular straight lines given by:

\[ ax^2 + 3xy - 2y^2 - 5x + 5y + c = 0 \]

we will follow these steps:

### Step 1: Identify the coefficients
The general form of the equation of a pair of straight lines is given by:

\[ Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0 \]

From the given equation, we can identify:
- \( A = a \)
- \( 2H = 3 \) (thus, \( H = \frac{3}{2} \))
- \( B = -2 \)
- \( 2G = -5 \) (thus, \( G = -\frac{5}{2} \))
- \( 2F = 5 \) (thus, \( F = \frac{5}{2} \))
- \( C = c \)

### Step 2: Use the condition for perpendicular lines
For the lines represented by the equation to be perpendicular, the following condition must hold:

\[ A + B = 0 \]

### Step 3: Substitute the values of A and B
Substituting the values we identified:

\[ a - 2 = 0 \]

### Step 4: Solve for \( a \)
Now, solve the equation:

\[ a = 2 \]

Thus, the value of \( a \) is \( 2 \).

### Final Answer
The value of \( a \) is \( 2 \).

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