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  • If t is the parameter for one end of a focal chord of the parabola ,

If t is the parameter for one end of a focal chord of the parabola \mathrm{ y^2=4 a x}, then its length is
 

Option: 1

\mathrm{a\left(t+\frac{1}{t}\right)^2}


Option: 2

\mathrm{ a\left(t-\frac{1}{t}\right)^2}


Option: 3

\mathrm{ a\left(t+\frac{1}{t}\right)}


Option: 4

\mathrm{ a\left(t-\frac{1}{t}\right)}


Answers (1)

best_answer

If \mathrm{t, t^{\prime}} are the ends of focal chord of parabola \mathrm{y^2=4 a x}, then its length =\mathrm{a\left(t^{\prime}-t\right)^2 }But for a focal chord \mathrm{t t^{\prime}=-1 }

\mathrm{\therefore \quad t^{\prime}=-\frac{1}{t} \quad }\\ \mathrm{\therefore \text { Required length }=a\left(-\frac{1}{t}-t\right)^2=a\left(t+\frac{1}{t}\right)^2 }

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