Question

From the point (-1,2), tangent lines are to the parabola `y^(2)=4x`. If the area of the triangle formed by the chord of contact and the tangents is A, then the value of `A//sqrt(2)` is ___________ .

Answer 1

Correct Answer - 8
(8) The chord of contact w.r.t point O(-1,2) is
`y=(x-1)" [Using "yy_(1)=2a(x+x_(1))]`
Solving y=x-1 with the parabola, we get the point of intersection as
`P(3+2sqrt(2),2+2sqrt(2))andQ(3-2sqrt(2),2-2sqrt(2))`
`:." "PQ^(2)=32+32=64`
`:." "PQ=8`
Also, the length of perpendicular from O(-1,2) on PQ is `4//sqrt(2)`.
Then the required area of triangle is
`A=(1)/(2)xx8xx((4)/(sqrt(2)))=8sqrt(2)` sq. units