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

1 Answer
Jul 18, 2016

Answer:

#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)#