What is the equation of the parabola with a focus at (15,-3) and a directrix of y= -4?

1 Answer
Shwetank Mauria
May 18, 2016

Equation of parabola is #x^2-30x-2y+218=0#

Explanation:

Here the directrix is a horizontal line #y=-4#.

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 #(15,-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-15)^2+(y+3)^2)# and from directrix will be #|y+4|#

Hence, #(x-15)^2+(y+3)^2=(y+4)^2#

or #x^2-30x+225+y^2+6y+9=y^2+8y+16#

or #x^2-30x-2y+234-16=0#

or #x^2-30x-2y+218=0#

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