What is the equation of the parabola with a focus at (10,19) and a directrix of y= 15?
1 Answer
Jan 19, 2018
Explanation:
#"from any point "(x,y)" on the parabola"#
#"the distance to the focus and the directrix from this point"#
#"are equal"#
#color(blue)"using the distance formula"#
#sqrt((x-10)^2+(y-19)^2)=|y-15|#
#color(blue)"squaring both sides"#
#(x-10)^2+(y-19)^2=(y-15)^2#
#rArr(x-10)^2cancel(+y^2)-38y+361=cancel(y^2)-30y+225#
#rArr(x-10)^2=8y-136#
#rArr(x-10)^2=8(y-17)larrcolor(blue)"is the equation"#
