What is the equation of the parabola with a focus at (2,1) and a directrix of y= 3?

1 Answer
Aug 14, 2017

#x^2-4x+4y-4=0#

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-2)^2+(y-1)^2)=|y-3|#

#color(blue)"squaring both sides"#

#(x-2)^2+(y-1)^2=(y-3)^2#

#rArrx^2-4x+4+y^2-2y+1=y^2-6y+9#

#rArrx^2-4xcancel(+y^2)cancel(-y^2)-2y+6y+4+1-9=0#

#rArrx^2-4x+4y-4=0larrcolor(red)" is the equation"#