What is the vertex form of the equation of the parabola with a focus at (12,22) and a directrix of #y=11 #?
1 Answer
Nov 24, 2017
Explanation:
#"the equation of a parabola in "color(blue)"vertex form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#
#"where "(h,k)" are the coordinates of the vertex and a"#
#"is a multiplier"#
#"for any point "(x.y)" on a parabola"#
#"the focus and directrix are equidistant from "(x,y)#
#"using the "color(blue)"distance formula "" on "(x,y)" and "(12,22)#
#rArrsqrt((x-12)^2+(y-22)^2)=|y-11|#
#color(blue)"squaring both sides"#
#rArr(x-12)^2+(y-22)^2=(y-11)^2#
#(x-12)^2cancel(+y^2)-44y+484=cancel(y^2)-22y+121#
#rArr(x-12)^2 =22y-363#
#rArry=1/22(x-12)^2+33/2larrcolor(red)"in vertex form"#