What is the equation of the parabola with a focus at (-1,3) and a directrix of y= -6?

1 Answer
May 18, 2016

Equation of parabola is #x^2+2x-18y-26=0#

Explanation:

Here the directrix is a horizontal line #y=-6#.

Since this line is perpendicular to the axis of symmetry, this is a regular parabola, where the #x# part is squared.

Now the distance of a point on parabola from focus at #(-1,3)# is always equal to its between the vertex and the directrix should always be equal. Let this point be #(x,y)#.

Its distance from focus is #sqrt((x+1)^2+(y-3)^2)# and from directrix will be #|y+6|#

Hence, #(x+1)^2+(y-3)^2=(y+6)^2#

or #x^2+2x+1+y^2-6y+9=y^2+12y+36#

or #x^2+2x-18y+10-36=0#

or #x^2+2x-18y-26=0#