What is the standard form of the equation of the parabola with a directrix at x=-9 and a focus at (-6,7)?

Question

1394 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-16T17:57:06

The equation is
${(y - 7)}^{2} = 6 (x + \frac{15}{2})$ $(y-7)^2=6(x+15/2)$

Any point $(x, y)$ $(x,y)$ is equidistant from the directrix and the focus.

$(x + 9) = \sqrt{{(x + 6)}^{2} + {(y - 7)}^{2}}$ $(x+9)=sqrt((x+6)^2+(y-7)^2)$

${(x + 9)}^{2} = {(x + 6)}^{2} + {(y - 7)}^{2}$ $(x+9)^2=(x+6)^2+(y-7)^2$

$x^{2} + 18 x + 81 = x^{2} + 12 x + 36 + {(y - 7)}^{2}$ $x^2+18x+81=x^2+12x+36+(y-7)^2$

$6 x + 45 = {(y - 7)}^{2}$ $6x+45=(y-7)^2$

The standard form is

${(y - 7)}^{2} = 6 (x + \frac{15}{2})$ $(y-7)^2=6(x+15/2)$

graph{((y-7)^2-6(x+(15/2)))=0 [-18.85, 13.18, -3.98, 12.04]}