A parabola can be drawn given a focus of #(3,-10)# and a directrix of #y=-6#. What is the equation of the parabola?
1 Answer
Sep 27, 2017
Explanation:
#"for any point "(x,y)" on the parabola"#
#"the distance from "(x,y)" to the focus and"#
#"the directrix are equal"#
#"using the "color(blue)"distance formula"#
#rArrsqrt((x-3)^2+(y+10)^2)=|y+6|#
#color(blue)"squaring both sides"#
#rArr(x-3)^2+(y+10)^2=(y+6)^2#
#x^2-6x+9cancel(+y^2)+20y+100=cancel(y^2)+12y+36#
#rArrx^2-6x+8y+73=0" is the equation"#
