Question

A parabola given by x = ay2 + by + c passes through points (1,2) , (-3,2) and (-2,4) .

1. Find the equation ?

2. Determine whether the line x + 2y + 3 = 0 is tangent to the parabola in (1)

3. Show that each point P(x,y) on the parabola is equidistant from (-2,2) and the line x= -4

Answer 1

The parabola has the form: $x=ay^2+by+c$. Substitute points $(1,2), (-3,2)$ and $(-2,4)$ into equation of parabola: $1=4a+2b+c,$ $-3=4a+2b+c$ and $-2=16a+4b+c$. We receive: $-3=1$ from the first and second equations. Thus, there is a mistake in the formulation of the problem. The points are not chosen correctly.