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The length of the chord of the parabola `x^2=4ay` passing through the vertex and having slope `tanalpha is `(a>0)`:A. 2 a cosec `alpha` cot `alpha`B. `4a tan alpha sec alpha`C. `4a cos alpha cot alpha`D. `4a sin alpha tan alpha` |
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Answer» Correct Answer - A Let A be the vertex and AP be a chord of `x^(2)=4"ay"` such that slope of AP is tan `alpha`. Let the coorddinates of P be `(2at, at^(2))` Then, `"Slope of AP"=(at^(2))/(2at)=t/2rArrtan alpha=t/2rArrt=2 tan alpha` `"Now, "` `APsqrt((2at-t)^(2)+(at^(2)-0)^(2))` `rArr" "AP=atsqrt(4+1^(2))=2a" tan"alphasqrt(4+4"tan"^(2)alpha)=4a tan alpha sec alpha` |
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