Find the joint equation of the pair of lines which pass through the origin and are perpendicular to the lines represented the equation `y^2+3x y-6x+5y-14=0`

Explanation

To find the joint equation of the pair of lines that pass through the origin and are perpendicular to the lines represented by the equation \( y^2 + 3xy - 6x + 5y - 14 = 0 \), we can follow these steps:

### Step 1: Simplify the Given Equation
We start with the equation:
\[ y^2 + 3xy - 6x + 5y - 14 = 0 \]
Since we are looking for lines that pass through the origin, we can ignore the constant term (-14) and focus on the terms that will help us find the lines through the origin:
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