# What is the equation in standard form of the parabola with a focus at (2,3) and a directrix of y= 9?

##### 1 Answer

Aug 30, 2017

#### Explanation:

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

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

#"are equal"#

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

#"with "(x,y)to(2,3)#

#rArrsqrt((x-2)^2+(y-3)^2)=|y-9|#

#color(blue)"squaring both sides"#

#(x-2)^2+(y-3)^2=(y-9)^2#

#rArrx^2-4x+4+y^2-6y+9=y^2-18y+81#

#rArrx^2-4x+12y-68=0#