The normal to a curve at `P(x, y)` meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a (1) ellipse (2) parabola (3) circle (4) hyperbola

Explanation

To solve the problem step-by-step, we need to analyze the given conditions and derive the equation of the curve.

### Step 1: Understand the given conditions
We have a point \( P(x, y) \) on the curve. The normal to the curve at this point meets the x-axis at point \( G \). The distance from the origin to point \( G \) is twice the abscissa (x-coordinate) of point \( P \).