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
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#
