Find the equation of the parabola whose focus is`(1,1)` and tangent at the vertex is `x+y=1.`

Explanation

To find the equation of the parabola with the given focus and tangent at the vertex, we can follow these steps:

### Step 1: Identify the given information
- Focus \( F(1, 1) \)
- Tangent at the vertex: \( x + y = 1 \)

### Step 2: Determine the slope of the tangent
The equation of the tangent can be rewritten in slope-intercept form:
...