Let PQ be a focal chord of the parabola `y^(2)=4ax`. The tangents to the parabola at P and Q meet at point lying on the line `y=2x+a,alt0`. If chord P

Question

Let PQ be a focal chord of the parabola `y^(2)=4ax`. The tangents to the parabola at P and Q meet at point lying on the line `y=2x+a,alt0`. If chord P

Let PQ be a focal chord of the parabola `y^(2)=4ax`. The tangents to the parabola at P and Q meet at point lying on the line
`y=2x+a,alt0`.
If chord PQ subtends an angle `theta` at the vertex of `y^(2)=4ax`, then `tantheta=`
A. `2sqrt(7)//3`
B. `-2sqrt(7)//3`
C. `2sqrt(5)//3`
D. `-2sqrt(5)//3`

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

Salim Ahmed Kawsar

Correct Answer - D
4 Angle made by chord PQ at vertex (0,0) is given by
`tantheta|(m_(OP)-m_(OQ))/(1+m_(OP)*m_(OQ))|((2//t)+2t)/(1-4)=(2{(1//t)+t})/(-3)=(-2sqrt(5))/(3)`

5 views Answered 2023-02-05 15:29