What is the equation in standard form of the parabola with a focus at (-1,18) and a directrix of y= 19?

1 Answer
Shwetank Mauria
Feb 8, 2017

y=−12x2−x

Explanation:

Parabola is the locus of a point, say (x,y), which moves so that its distance from a given point called focus and from a given line called directrix , is always equal.

Further, standard form of equation of a parabola is y=ax2+bx+c

As focus is (−1,18), distance of (x,y) from it is √(x+1)2+(y−18)2

and distance of (x,y) from directrix y=19 is (y−19)

Hence equation of parabola is

(x+1)2+(y−18)2=(y−19)2

or (x+1)2=(y−19)2−(y−18)2=(y−19−y+18)(y−19+y−18)

or x2+2x+1=−1(2y−1)=−2y+1

or 2y=−x2−2x

or y=−12x2−x
graph{(2y+x^2+2x)(y-19)=0 [-20, 20, -40, 40]}

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