The length of the chord of the parabola `x^2=4ay` passing through the vertex and having slope `tanalpha is `(a>0)`:

Options

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`

Answer

A

Explanation

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`