Question

A tangent is drawn to the parabola y^2=4x at the point P whose abscissa lies in the interval [1,4]. The maximum possible area of the triangle formed by the tangent at P,ordinate of point P and the x-axis is equal to?
(ans=16)

Answer 1

So,

Area=

2

1

×2t×2t

2

=2t

3

And maximum value of t from (1) =2

Area=2×(2)

3

=2×8=16sq.units