# 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"#