Answer:
The parabola obtained is x=y²
Step-by-step explanation:
Given the focus (1/4,0) and directrix: x=-1/4
A point on the parabola is determined by the distance of that point with the focus and with the directrix:
Distance between the parabola and the directrix:[tex]\sqrt{(x+\frac{1}{4})^{2} }[/tex]
Distance between the parabola and the focus:[tex]\sqrt{(x-\frac{1}{4})^{2} +(y-0)^{2} }[/tex]
[tex]\sqrt{(x+\frac{1}{4})^{2}}[/tex]=[tex]\sqrt{(x-\frac{1}{4})^{2} +(y-0)^{2} }[/tex]
[tex](x+\frac{1}{4})^{2}[/tex]=[tex](x-\frac{1}{4})^{2} +(y-0)^{2} [/tex]
[tex]x^2+\frac{1}{2} x+\frac{1}{16} = x^2-\frac{1}{2} x+\frac{1}{16} + y^{2}[/tex]
[tex]\frac{1}{2} x=-\frac{1}{2} x + y^{2}[/tex]
[tex]\frac{1}{2} x+\frac{1}{2} x = y^{2}[/tex]
x=y²
