Let p be the parabola with focus (0,4) and directrix y=x. write an equation whose graph is a parabola with a vertical directrix that is congruent to p.

y²=4√2.x

Step-by-step explanation:

The focus is at (0,4) and directrix is y=x or x-y =0, for a parabola P.

The distance between the focus and the directrix of the parabola P is

=

{Since the perpendicular distance of a point (x1, y1) from the straight line ax+by+c =0 is given by }

Let us assume that the equation of the parabola which is congruent with parabola P is y²=4ax

{Since the parabola has vertical directrix}

Hence, the distance between focus and the directrix is 2a = , {Two parabolas are congruent when the distances between their focus and the directrix are same}

⇒ a=√2

Therefore, the equation of the parabola is y²=4√2.x (Answer)

answer: sine

step-by-step explanation:

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