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

Question

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

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^(@)`

Monjur Alahi

5 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 - 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^(@)`