Find the value of `a` for which the lines represented by `a x^2+5x y+2y^2=0` are mutually perpendicular.

Explanation

To find the value of \( a \) for which the lines represented by the equation \( ax^2 + 5xy + 2y^2 = 0 \) are mutually perpendicular, we can follow these steps:

### Step 1: Understand the condition for perpendicular lines
For two lines represented by the general quadratic equation \( Ax^2 + Bxy + Cy^2 = 0 \) to be mutually perpendicular, the condition is:
\[ B^2 = 4AC \]
Where \( A \), \( B \), and \( C \) are the coefficients of \( x^2 \), \( xy \), and \( y^2 \) respectively.
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