If the lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.

Explanation

To find the equation of the circle given the lines \(2x - 3y = 5\) and \(3x - 4y = 7\) as diameters and an area of 154 square units, we can follow these steps:

### Step 1: Find the intersection point of the two lines
The intersection point of the two lines will give us the center of the circle. We need to solve the equations simultaneously.

1. The first line is:
\[
2x - 3y = 5 \quad \text{(Equation 1)}
...