Question

How do you write an equation for the parabola with Vertex at the origin, focus at ( 0, 1/11)?

Answer 1

`color(red)(11x^2=4y)`

Explanation:

Given that the vertex of parabola is origin `(color(red)(0,0))` and focus `(color(red)(0,1/11))`.So the directrix of the parabola will be perpendicular to y-axis and will pass through `(color(red)(0,-1/11))`.Hence its equation will be `color(blue)(y=-1/11)`.

Let `(color(green)(h,k))` be the coordinate of any point on the parabola.

So by definition of parabola

`"Dist.of(h,k) from focus"="Dist. of(h,k) from directrix"`

`sqrt(h^2+(k-1/11)^2)=(k+1/11)`

`=>(h^2+(k-1/11)^2)=(k+1/11)^2`

`=>h^2=(k+1/11)^2-(k-1/11)^2`

`=>h^2=4*k*1/11`

`=>11h^2=4k`

Substituting x for and y for k we get the equation of the parabola as follows.

Equation of parabola

`color(red)(11x^2=4y)`