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Find the area of the parabola y^(2)=4ax ...

Find the area of the parabola `y^(2)=4ax` bounded by its latus rectum.

Text Solution

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Given parabola is `y^2=4a x`
its focus is `(a,0)`
equation of latus rectum is `x=a`
the parabola is symmetrical about the x-axis
Required area `=2int_0^a (y)dx`
`= 2int_0^a sqrt(4ax) dx`
`= 2(2sqrt(a))int_0^a x^(1/2) dx`
`= 4sqrt(a) [ x^(3/2) /((3)/(2)) ]_ 0^4`
`= (4sqrt(a)) 2/(3) a^(3/2)`
`= 8/(3) a^2` sq.units
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