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PSQ is a focal chord of a parabola whose...

PSQ is a focal chord of a parabola whose focus is S and vertex is A. PA, QA, are produced to meet the dirrecterix in R and T. Then `/_RST` is equal to

A

`30^(@)`

B

`90^(@)`

C

`60^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
(2) Let `P-=(at_(1)^(2),2at_(1))andQ-=(at_(2)^(2),2at_(2))`.
`rArrt_(1)t_(2)=-1`
Equation of AP is `y=(2)/(t_(1))x_(1)`.
`rArrR-=(-a,-2a//t_(1))`
Similarly, `T-=(-a,(-2a)/(t_(2)))`
Slope of RS `=(((-2a)/(t_(1))))/(2a)=-(1)/(t_(2))`
Slope of TS `=(((-2a)/(t_(2))))/(2a)=-(1)/(t_(2))`
Now, `(-(1)/(t_(1)))xx(-(1)/(t_(2)))=(1)/(t_(1)t_(2))=-1`
`rArr" "angleRST=90^(@)`
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