# Find the equation of the parabola having its focus(2,0) and directrix x=-2. Then find the length of the latus rectum.

1
by danica09

Log in to add a comment

by danica09

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

In this case, we can assume that the parabola's focus is located at the right side, in the x-axis, and the directrix at the left side 2 units away from the vertex of parabola meaning the parabola is facing to the right.

vertex:(0,0)

directrix:x=-2

focus:(2,0)

equation of parabola facing to the right:

y=4ax

To find a, it is the distance of the focus from the vertex, meaning if you graph it, it is 2 units away.. so:

a=2

Now substitute:

y=4ax

y=4(2)x

y=8x

After finding the equation of the parabola, find the length of the latus rectum, which the formula is:

LR=4a

substitute the value of a

:LR=4(2)

LR=8 units

Hope this helps =)

vertex:(0,0)

directrix:x=-2

focus:(2,0)

equation of parabola facing to the right:

y=4ax

To find a, it is the distance of the focus from the vertex, meaning if you graph it, it is 2 units away.. so:

a=2

Now substitute:

y=4ax

y=4(2)x

y=8x

After finding the equation of the parabola, find the length of the latus rectum, which the formula is:

LR=4a

substitute the value of a

:LR=4(2)

LR=8 units

Hope this helps =)