What is the equation of the parabola with a focus at (3,18) and a directrix of y= -21?

1 Answer
Jul 29, 2017

#78y=x^2-6x-108#

Explanation:

Parabola is the locus of a pint, which moves so that its distance from a point called focus and a line called directrix is always equal.

Let the point on parabola be #(x,y)#,

its distance from focus #(3,18)# is

#sqrt((x-3)^2+(y-18)^2)#

and distance from directrix #y-21# is #|y+21|#

Hence equation of parabola is, #(x-3)^2+(y-18)^2=(y+21)^2#

or #x^2-6x+9+y^2-36y+324=y^2+42y+441#

or #78y=x^2-6x-108#

graph{(x^2-6x-78y-108)((x-3)^2+(y-18)^2-2)(x-3)(y+21)=0 [-157.3, 162.7, -49.3, 110.7]}