Danica09idn
Answered

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

Sagot :

Jers15idn
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 =)
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