Write equations of parabolas from properties Geometry

Find the equation of the parabola whose focus is \left(2{,}2\right) and directrix is y=4.

y= -\dfrac{1}{4}x^2+x+2

y= \dfrac{1}{4}x^2-x+2

y= x^2+x+8

y= -x^2+x+8

Find the equation of the parabola whose focus is \left(-1{,}3\right) and directrix is y=1.

y=\dfrac{1}{4}x^2+\dfrac{1}{2}x+\dfrac{9}{4}

y= -\dfrac{1}{6}x^2-\dfrac{1}{5}x-\dfrac{7}{5}

y=- \dfrac{1}{6}x^2-\dfrac{1}{3}x+\dfrac{3}{2}

y=-\dfrac{1}{4}x^2-\dfrac{1}{2}x+\dfrac{9}{2}

Find the equation of the parabola whose focus is \left(0{,}2\right) and directrix is y=-1.

y=\dfrac{1}{6}x^2+\dfrac{1}{2}

y=- \dfrac{1}{4}x^2+\dfrac{3}{7}

y= \dfrac{1}{4}x^2+\dfrac{7}{3}

y=\dfrac{1}{6}x^2-\dfrac{1}{2}

Find the equation of the parabola whose focus is \left(2{,}0\right) and directrix is y=3.

y= -\dfrac{1}{6}x^2+\dfrac{2}{3}x+\dfrac{5}{6}

y= \dfrac{1}{6}x^2+\dfrac{2}{3}x-\dfrac{5}{6}

y= -\dfrac{1}{6}x^2-\dfrac{3}{2}x+\dfrac{5}{6}

y= \dfrac{1}{6}x^2+\dfrac{2}{3}x+\dfrac{6}{5}

Find the equation of the parabola whose focus is \left(-1{,}2\right) and directrix is x=1.

x= -\dfrac{1}{4}y^2+y-1

x= -\dfrac{1}{4}y^2-y-2

x= \dfrac{1}{4}y^2+y-2

x= -\dfrac{1}{4}y^2-y+1

Find the equation of the parabola whose focus is \left(1{,}4\right) and directrix is x=-1.

x=\dfrac{1}{4}y^2-2y+4

x=\dfrac{1}{8}y^2-2y-4

x=-\dfrac{1}{8}y^2+2y-4

x=-\dfrac{1}{4}y^2-2y-4

Find the equation of the parabola whose focus is \left(2,-1\right) and directrix is x=3.

x= -\dfrac{1}{2}y^2-y+2

y= \dfrac{1}{4}x^2-x+2

y= -\dfrac{1}{4}x^2-x-2

x= -\dfrac{1}{2}y^2+y-2