# What is the equation in standard form of the parabola with a focus at (11,-5) and a directrix of y= -19?

##### 1 Answer

Dec 3, 2017

#### Explanation:

#"for any point "(x,y)" on the parabola"#

#"the focus and directrix are equidistant "#

#color(blue)"using the distance formula"#

#sqrt((x-11)^2+(y+5)^2)=|y+19|#

#color(blue)"squaring both sides"#

#(x-11)^2+(y+5)^2=(y+19)^2#

#rArrx^2-22x+121cancel(+y^2)+10y+25=cancel(y^2)+38y+361#

#rArr-28y=-x^2+22x+215#

#rArry=1/28x^2-11/14x-215/28#