If `(a ,b)` is the midpoint of a chord passing through the vertex of the parabola `y^2=4(x+1),` then prove that `2(a+1)=b^2`.

Explanation

To prove that if \((a, b)\) is the midpoint of a chord passing through the vertex of the parabola \(y^2 = 4(x + 1)\), then \(2(a + 1) = b^2\), we will follow these steps:

### Step 1: Identify the Vertex of the Parabola
The given equation of the parabola is \(y^2 = 4(x + 1)\). The vertex form of a parabola is given by \(y^2 = 4p(x - h)\), where \((h, k)\) is the vertex.

From the equation, we can see that:
- The vertex is at \((-1, 0)\).

...