# What is the standard form of the equation of the parabola with a directrix at x=3 and a focus at (-5,5)?

##### 1 Answer

Sep 6, 2017

#### Explanation:

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

#"the distance from "(x,y)" to the focus and directrix"#

#"are equal"#

#rArrsqrt((x+5)^2+(y-5)^2)=|x-3|#

#color(blue)"squaring both sides"#

#(x+5)^2+(y-5)^2=(x-3)^2#

#rArrcancel(x^2)+10x+25+y^2-10y+25=cancel(x^2)-6x+9#

#rArry^2-10y+6x+41=0larrcolor(red)" is the equation"#