1.

Let PQ be a focal chord of the parabola y^(2) = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a,a gt 0. If chord PQ subtends an angle theta at the vertex of y^(2) = 4ax, then tan theta is equal to

Answer»

`(2)/(3) SQRT(7)`
`(-2)/(3) sqrt(7)`
`(2)/(3) sqrt(5)`
`(-2)/(3) sqrt(5)`

SOLUTION :`m_(OP) = (2at - 0)/(at^(2) - 0) = (2)/(t)`

`m_(OQ) = (-2a//t)/(a//t^(2)) = - 2T`
`:. TAN theta = ((2)/(t) + 2t)/(1 - (2)/(t).2t) = (2(t - (1)/(t)))/(1 - 4) = (-2 sqrt(5))/(3)`
Where `t + (1)/() = sqrt(5)`


Discussion

No Comment Found

Related InterviewSolutions