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Question
If the line y = mx + 1 is tangent to the parabola y2 = 4x then find the value of m.
Solution
Given that y2 = 4x ......(i)
And y = mx + 1 .....(ii)
From equation (i) and (ii) we get
(mx + 1)2 = 4x
⇒ m2x2 + 1 + 2mx – 4x = 0
⇒ m2x2 + (2m – 4)x + 1 = 0
Applying condition of tangency, we have
(2m – 4)2 – 4m2 × 1 = 0
⇒ 4m2 + 16 – 16m – 4m2 = 0
⇒ – 16m = – 16
⇒ m = 1
Hence, the required value of m is 1.
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