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Question

# 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

A

(3, 8)

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B

(1, 5)

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C

(2, 3)

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D

(4, 6)

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Solution

## The correct option is C (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)

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