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If the line y = mx + 1 is tangent to the parabola y2 = 4x then find the value of m.
Answers (1)
Given that line y=mx+1 is tangent to the parabola y2=4x
Solving line with parabola we have
(mx+1)2=4x
m2x2+2mx+1=4x
m2x2+x(2m-4)+1=0
Since the line touches the parabola, above equation must have equal roots.
Discriminant D=0
(2m-4)2-4m2=0
4m2-16m+16-4m2=0
16m=16
m=1
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