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 `D

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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 `D

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.
A. `anglePRQ=(pi)/(2)`
B. the point R is `(4,4)`
C. the point R is `((1)/(4),1)`
D. None of these

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
`(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)`