1.

Let P(4,-4) and Q(9,6) be points on the parabola y^(2)=4a(x-b). Let R be a point on the arc of the parabola between P and Q. Then the area of DeltaPQR is largest when.

Answer»

`anglePRQ=(pi)/(2)`
the POINT R is `(4,4)`
the point R is `((1)/(4),1)`
NONE of these

Solution :`(4,-4)` and `(9,6)` lie on `y^(2)=4A(x-b)`
`implies 16=4a(4-b)` and `36=4a(9-b)impliesa=1,b=0`
`therefore` Equation of PARABOLA is `y^(2)=4x`
Let the point R be `(t^(2),2T)`, where `t in(-2,3)`
`thereforeDeltaPQR=(1)/(2)|(4,-4,1),(9,6,1),(t^(2),2t,1)|`
`DeltaPQR=(1)/(2)|10t-10t^(2)+60|=(1)/(4)|125-5(2t-1)^(2)|`
`therefore` Area is largest when `t=(1)/(2){becauset in (-2,3)}`
`thereforeR(t^(2),2t)=R((1)/(4),1)`


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