The point of intersection of the tengents to the parabola y2=4x at the points, where the parameter 't' has the value 1 and 2, is
(2, 3)
Slope of the tanget to a parabola at t is 1t. The equations of tangents at t1 and t2 are
y−2at1=1t1(x−at21) .....(i)y−2at1=1t1(x−at21) .....(ii)
Solving (i) and (ii), the point of intersection is (at1t2, a(t1+t2)) where t1=1 and t2=2. Here a=1.
Hence the required point is (2,3)