What is the standard form of the equation of the parabola with a directrix at x=-6 and a focus at (12,-5)?

1 Answer
Sep 10, 2017

#y^2+10y-36x+133=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"#

#sqrt((x-12)^2+(y+5)^2)=|x+6|#

#color(blue)"squaring both sides"#

#(x-12)^2+(y+5)^2=(x+6)^2#

#rArrcancel(x^2)-24x+144+y^2+10y+25=cancel(x^2)+12x+36#

#rArry^2+10y-36x+133=0#