What is the equation of the quadratic graph with a focus of #(-4, 17/8)# and a directrix of #y=15/8#?

1 Answer
Jim G.
Jan 9, 2018

#(x+4)^2=1/2(y-2)#

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"#

#rArrsqrt((x+4)^2+(y-17/8)^2)=|y-15/8|#

#color(blue)"squaring both sides"#

#(x+4)^2+(y-17/8)^2=(y-15/8)^2#

#rArr(x+4)^2cancel(+y^2)-34/8y+289/64=cancel(y^2)-30/8y+225/64#

#rArr(x+4)^2=-30/8y+34/8y+225/64-289/64#

#rArr(x+4)^2=1/2y-1#

#rArr(x+4)^2=1/2(y-2)larrcolor(blue)"is the equation"#

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