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Let P(4, -4) and Q(9, 6) be two points o...

Let P(4, -4) and Q(9, 6) be two points on the parabola, `y^(2)=4x` and let X be any point on the are POQ of this parabola, where O is the vertex of this parabola, such that the area of `DeltaPXQ` is maximum. Then this maximum area (in sq. units) is

A

`31 3/4`

B

`30 1/2`

C

`32`

D

`31 1/4`

Text Solution

Verified by Experts

The correct Answer is:
D

`"The line AB is The distance of C from AB is :"`
`y+4=(10)/(5)(x-4)" "f(t)=(|2t^(2)-2t-12|)/(sqrt5)`
`y+4=2x-8" "=2(|(t-1//2)^(2)-(25)/(4)|)/(sqrt5)`
`" and "0let^(2)le 9 and -4 le 2t le 6`
`f(t)_("max")=t in [-2, 3] =2(25)/(4sqrt5)," Max area "rArr 2(25)/(4sqrt5)=(125)/(4)" sq. units."`
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