If a line `y=3x+1` cuts the parabola `x^2-4x-4y+20=0` at `Aa n dB ,` then the tangent of the angle subtended by line segment `A B` at the origin is `(

Question

If a line `y=3x+1` cuts the parabola `x^2-4x-4y+20=0` at `Aa n dB ,` then the tangent of the angle subtended by line segment `A B` at the origin is `(

If a line `y=3x+1` cuts the parabola `x^2-4x-4y+20=0` at `Aa n dB ,` then the tangent of the angle subtended by line segment `A B` at the origin is `(8sqrt(3))/(205)` (b) `(8sqrt(3))/(209)` `(8sqrt(3))/(215)` (d) none of these
A. `8sqrt(3)//205`
B. `8sqrt(3)//209`
C. `8sqrt(3)//215`
D. none of these

Monjur Alahi

7 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 - B
(2) The joint equation of OA and OB is
`x^(2)-4x(y-3x)-4y(y-3x)+20(y-3x)^(2)=0`
(Making the equation of the parabola homogeneous using straight line)
`or193x^(2)+16y^(2)-112xy=0`
`tantheta=(2sqrt(h^(2)-ab))/(a+b)`
`=(2sqrt(56^(2)-193xx16))/(193+16)`
`=(8sqrt(3))/(209)`

7 views Answered 2023-02-05 15:29