`T P` and `T Q` are tangents to the parabola `y^2=4a x` at `Pa n dQ ,` respectively. If the chord `P Q` passes through the fixed point `(-a ,b),` then

Question

`T P` and `T Q` are tangents to the parabola `y^2=4a x` at `Pa n dQ ,` respectively. If the chord `P Q` passes through the fixed point `(-a ,b),` then

`T P` and `T Q` are tangents to the parabola `y^2=4a x` at `Pa n dQ ,` respectively. If the chord `P Q` passes through the fixed point `(-a ,b),` then find the locus of `Tdot`

Monjur Alahi

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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 - by = 2a (x-a)
Let the point T be (h,k).
Equation of chord of contact to parabola `y^(2)=4ax` w.r.t. T is
ky=2a(x+h)
It passes through the point (-a,b).
`:." "bk=2a(-a+h)`
So, locus of point T is by=2a (x-a).

4 views Answered 2023-02-05 15:29