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 can follow the reasoning presented in the video transcript. Here's a structured solution:

### Step 1: Understanding the Problem
We need to find the nature of a curve given that the normal at point \( P(x, y) \) meets the x-axis at point \( G \), and the distance from \( G \) to the origin is twice the abscissa of \( P \).

### Step 2: Equation of the Normal
The equation of the normal to the curve at point \( P(x, y) \) can be expressed using the point-slope form of a line. The slope of the normal is the negative reciprocal of the derivative \( \frac{dy}{dx} \) at that point.

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