What is the equation in standard form of the parabola with a focus at (11,-5) and a directrix of y= -19?

1 Answer
Jim G.
Dec 3, 2017

y=1/28x^2-11/14x-215/28

Explanation:

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

"the focus and directrix are equidistant "

color(blue)"using the distance formula"

sqrt((x-11)^2+(y+5)^2)=|y+19|

color(blue)"squaring both sides"

(x-11)^2+(y+5)^2=(y+19)^2

rArrx^2-22x+121cancel(+y^2)+10y+25=cancel(y^2)+38y+361

rArr-28y=-x^2+22x+215

rArry=1/28x^2-11/14x-215/28

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