Are the two parabolas defined below similar or congruent or both? justify your reasoning. parabola 1: the parabola with a focus of (0,2) and a directrix line of y= −4. parabola 2: the parabola that is the graph of the equation y=(1/6)x².

They are similar by a factor of 14

Step-by-step explanation:

From the general equation of a parabola opening up (since the directrix is on the y axis and the focus is upwards this line) the focus coordinates are:

So h=0 and k+p=2, for the directrix:

solving k and p from the two equations above:

So for Parabola 1 the equation would be:

For Parabola 2 the general equation is:

here h=0, k=0, p=3/2 so focus is (0,3/2), directix is y=-3/2, they have the same orientation.

they are not congruent. For them to be similar it must comply:

replacing and solving for k:

They are similar by a factor of 14