The orthocentre of the triangle formed by the lines `2x^(2)+3xy-2y^(2)-9x+7y-5=0` with `4x+5y-3=0` is

Options

A. `(3//5,11//5)`
B. `(6//5,11//5)`
C. `(5//6,11//5)`
D. `(3//5,6//5)`

Explanation

To solve the problem of finding the orthocentre of the triangle formed by the lines \( 2x^2 + 3xy - 2y^2 - 9x + 7y - 5 = 0 \) and \( 4x + 5y - 3 = 0 \), we will follow these steps:

### Step 1: Identify the lines
The first equation \( 2x^2 + 3xy - 2y^2 - 9x + 7y - 5 = 0 \) represents a pair of straight lines. We need to factor this equation to find the lines it represents.