What is the standard form of the equation of the parabola with a focus at (1,-2) and a directrix of #y= 9#?

1 Answer
Jim G.
Feb 11, 2018

#y=-1/22x^2+1/11x+38/11#

Explanation:

#"for any point "(x,y)" on the parabola"#

#"the distance from "(x,y)" to the focus and directrix"#
#"are equal"#

#"using the "color(blue)"distance formula"#

#sqrt((x-1)^2+(y+2)^2)=|y-9|#

#color(blue)"squaring both sides"#

#(x-1)^2+(y+2)^2=(y-9)^2#

#x^2-2x+1cancel(+y^2)+4y+4=cancel(y^2)-18y+81#

#rArr-22y+77=x^2-2x+1#

#rArr-22y=x^2-2x-76#

#rArry=-1/22x^2+1/11x+38/11larrcolor(red)"in standard form"#

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