Answer:
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
[tex]\frac{ |0-4| }{\sqrt{(1)^{2}+(-1)^{2} } }[/tex]=[tex]\frac{4}{\sqrt{2} }[/tex]
{Since the perpendicular distance of a point (x1, y1) from the straight line ax+by+c =0 is given by [tex]\frac{ |ax1+by1+c| }{\sqrt{a^{2}+b^{2} } }[/tex] }
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 = [tex]\frac{4}{\sqrt{2} }[/tex], {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)
