If the line `y=3x+c` touches the parabola `y^2=12 x` at point `P` , then find the equation of the tangent at point `Q` where `P Q` is a focal chord.

If the line `y=3x+c` touches the parabola `y^2=12 x` at point `P` , then find the equation of the tangent at point `Q` where `P Q` is a focal chord.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Correct Answer - `x+3y+27=0`
Line `(1)/(3)y=x+(c)/(3)` touches the parabola `y^(2)=12x`.
Let us compare this line `ty=x+at^(2)orty=x+3t^(2)`.
So, we have `t=(1)/(3)` which is parameter of point P.
Since PQ is focal chord, parameter of point Q is -3.
Therefore, equation of tangent at Q is
`(-3)y=x+3(-3)^(2)`
`or" "x+3y+27=0`

5 views Answered 2023-02-05 15:29

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