What is the equation of the parabola with a focus at (9,12) and a directrix of y= -13?

1 Answer
Shwetank Mauria
Nov 7, 2017

#x^2-18x-50y+56=0#

Explanation:

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

Let the point be #(x,y)#. Its distance from focus #(9,12)# is

#sqrt((x-9)^2+(y-12)^2)#

and its distance from directrix #y=-13# i.e. #y+13=0# is #|y+13|#

hence equation is

#sqrt((x-9)^2+(y-12)^2)=|y+13|#

and squaring #(x-9)^2+(y-12)^2=(y+13)^2#

or #x^2-18x+81+y^2-24y+144=y^2+26y+169#

or #x^2-18x-50y+56=0#

graph{(x^2-18x-50y+56)((x-9)^2+(y-12)^2-1)(y+13)=0 [-76.8, 83.2, -33.44, 46.56]}

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