What is the equation in standard form of the parabola with a focus at (-10,-47) and a directrix of y= -5?

Question

1490 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-05T09:32:54

${(x + 10)}^{2} = - 84 (y + 26)$ $(x+10)^2=-84(y+26)$ , revealing that

the vertex is V(-10, -26) and the axis is #x=-10 (downwards)..

Use

distance PS of P(x, y) on the parabola from its focus $S (- 10, - 47)$ $S(-10, -47)$

= its perpendicular distance PN from the directrix $y = - 5$ $y=-5$

$P S = \sqrt{{(x + 10)}^{2} + {(y + 47)}^{2}} = P N = \pm (y - (- 5 +)$ $PS=sqrt((x+10)^2+(y+47)^2) = PN =+-(y-(-5+)$ .

Squaring and equating,

${(x + 10)}^{2} = - 84 y - 2286$ $(x+10)^2=-84y-2286$ In the standard form,

${(x + 10)}^{2} = - 84 (y + 26)$ $(x+10)^2=-84(y+26)$ revealing that

the vertex is V(-10, -26) and the axis is #x=-10 (downwards).