Q19 of 63 Page 202

If the line y = mx + 1 is tangent to the parabola y2 = 4x then find the value of m.

Solving the given equations,


y = mx + 1 & y2 = 4x


(mx + 1)2 = 4x


m2x2 + 2mx + 1 = 4x


m2x2 + 2mx – 4x + 1 = 0


m+x2 + x (2m – 4) + 1 = 0


As the line touches the parabola, above equation must have equal roots,


Discriminant (D) = 0


(2m – 4)2 - 4 (m2) (1) = 0


4m2 - 16m + 16 – 4m2 = 0


-16 m + 16 = 0


- m + 1 = 0


m = 1


Hence, the required value of m is 1.


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