Question #3f383

1 Answer
Jim G.
Nov 20, 2017

#y=-1/12x^2#

Explanation:

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

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

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

#rArrsqrt((x-0)^2+(y+3)^2)=|y-3|#

#color(blue)"squaring both sides"#

#x^2+(y+3)^2=(y-3)^2#

#rArrx^2+y^2+6y+9=y^2-6y+9#

#rArrx^2cancel(+y^2)cancel(-y^2)+6y+6ycancel(+9)cancel(-9)=0#

#rArr12y=-x^2#

#rArry=-1/12x^2larrcolor(red)"is the equation"#
graph{(y+1/2x^2)((x-0)^2+(y+3)^2-0.05)(y-0.001x-3)=0 [-10, 10, -5, 5]}

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