How do we find the latus rectum of the parabola #y=2x^2#?

1 Answer
Jul 28, 2017

Answer:

Latus rectum is #1/2#.

Explanation:

Vertex form of equation of paarbola is #y=a(x-h)^2+k#, where vertex is #(0,0)# and #x=h# is the axis of symmetry. In the equation #y=a(x-h)^2+k#, focus is #(h,k+1/(4a))# and directrix is #y=k-1/(4a)#.

As such for #y=2x^2=2(x-0)^2+0#, while vertex is #(0,0)#

focus are #(0,0+1/8)# or #(0,1/8)# andpoints on latus rectum would be on bothsides of parabola from focus.

As #y=1/8# gives #x=+-1/4#, which means points of the latus rectum are #(-1/4,1/8)# and #(1/4,1/8)#

and latus rectum is #1/2#.

graph{(y-2x^2)(x^2+(y-1/8)^2-0.0001)((x+1/4)^2+(y-1/8)^2-0.0001)((x-1/4)^2+(y-1/8)^2-0.0001)=0 [-0.628, 0.622, -0.0875, 0.5375]}