Question #46d00

Question

2184 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-30T18:12:47

The distance between any point, $(x,y)$ on the parabola and the focus $(0,1)$ is:

$d = sqrt((x - 0)^2 + (y - 1)^2)$

The distance any point, $(x,y)$ , on the parabola and the line $y = -1$ is:

$d = sqrt((y - (-1))^2)$

Because the definition of the parabola requires that these two distances be equal, we can set the right sides of both equations equal:

$sqrt((x - 0)^2 + (y - 1)^2) = sqrt((y - (-1))^2)$

Square both sides of the equation and convert the -- to a +:

$(x - 0)^2 + (y - 1)^2 = (y +1)^2$

Expand the squares:

$x^2 + y^2 -2y+1 = y^2 + 2y+ 1$

Combine like terms:

$4y = x^2$

Divide both sides by 4:

$y = 1/4x^2$

The derivation is complete.