Two straight lines pass through the fixed points `(+-a, 0)` and have slopes whose products is `pgt0` Show that the locus of the points of intersection of the lines is a hyperbola.

Explanation

To show that the locus of the points of intersection of two lines passing through the fixed points \((\pm a, 0)\) with slopes whose product is \(p > 0\) is a hyperbola, we can follow these steps:

### Step 1: Set up the equations of the lines
Let the slopes of the two lines be \(m_1\) and \(m_2\). The equations of the lines passing through the points \((a, 0)\) and \((-a, 0)\) can be written as:

1. For the first line through \((a, 0)\):
\[
y - 0 = m_1(x - a) \implies y = m_1 x - m_1 a
...