If m is a variable, then prove that the locus of the point of intersection of the lines `x/3-y/2=m and x/3+y/2=1/m` is a hyperbola.

Options

A. parabola
B. ellipse
C. hyperbola
D. none of these

Explanation

To prove that the locus of the point of intersection of the lines \( \frac{x}{3} - \frac{y}{2} = m \) and \( \frac{x}{3} + \frac{y}{2} = \frac{1}{m} \) is a hyperbola, we can follow these steps:

### Step 1: Write the equations of the lines
We have two equations:
1. \( \frac{x}{3} - \frac{y}{2} = m \) (Equation 1)
2. \( \frac{x}{3} + \frac{y}{2} = \frac{1}{m} \) (Equation 2)

### Step 2: Multiply the two equations
...