Answer:
Answer is option D) y= [tex]\frac{1}{4}(x-1)^{2}[/tex]
Step-by-step explanation:
Quadratic graph with a focus and a directrix is a parabola as in the picture attached.
Now we assume a point (x,y) is given on the parabola.Focus of parabola be the point O(1,1) and the directrix y=(-1)
As we know that in a parabola distance OP is equal to the distance between P and directrix y=(-1)
Therefore OP = distance from directrix y = (-1)
[tex]\sqrt{(x-1)^{2}+(x-1)^{2}[/tex] = [tex]\sqrt{(y+1)^{2}[/tex]
[tex](x-1)^{2} +(y-1)^{2} = (y+1)^{2}[/tex]
[tex]y^{2}-2y+1+x^{2}-2x+1=y^{2}+2y+1[/tex]
[tex]1-2y+x^{2}-2x=2y[/tex]
[tex]1+x^{2}-2x=4y[/tex]
[tex]y=\frac{1}{4}(x-1)^{2}[/tex]
