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  • 19. If the line y = mx + 1 is tangent to the parabola y^2 = 4x then find the value of m.

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

Posted by

infoexpert22

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