The tangents to the parabola y² = 4x at the points (1,2) and (4,4) meets on the line :-
(A) x = 3
(B) y = 3
(C) x + y = 4
(D) none of these
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y^2 = 4x
2y dy/dx = 4.
Slope of tangent at (x1,y1) = 2/y1.
Tangent T1 at (1,2): (y-2)/(x-1)=2/2
Or y = 2x
Tangent T2 at (4,4) : (y-4)/(x-4)=2/4.
Or 2y = x+4.
Intersection P of tangents: (4/3,8/3).
So P lies on x+y = 4.
2y dy/dx = 4.
Slope of tangent at (x1,y1) = 2/y1.
Tangent T1 at (1,2): (y-2)/(x-1)=2/2
Or y = 2x
Tangent T2 at (4,4) : (y-4)/(x-4)=2/4.
Or 2y = x+4.
Intersection P of tangents: (4/3,8/3).
So P lies on x+y = 4.
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