Question

Under what conditions might two parabolas be congruent? Explain your reasoning.

Answer 1

If the sequence of rigid motion is exist that take one parabola onto the other then both parabolas are said to be congruent.

Also, two parabolas are said to be congruent if two points are at equal distance for the focus point. The two parabolas are congruent if they have same shape and they have same distance between focus and directrix.

Answer 2

when same distance between the focus and Directrix

Explanation:

we know that when two parabola will be congruent if we find 2 point are at equal distance from focus point

so as if we align vertices and we get parallel and parabola open in same direction

and we know the parabola have same shape when focus and Directrix are aligned

so as that 2 parabola will congruent when they have the same distance between the focus and Directrix