Maths-
General
Easy

Question

If two tangents drawn from the point (alpha comma beta) to the parabola y2 = 4x be such that the slope of one tangent is double of the other then

  1. beta = fraction numerator 2 over denominator 9 end fraction blank alpha 2    
  2. alpha = fraction numerator 2 over denominator 9 end fraction blank beta 2    
  3. 2alpha = 9beta 2    
  4. none of these    

The correct answer is: alpha = fraction numerator 2 over denominator 9 end fraction blank beta 2


    To find the relation between alpha comma beta
    y equals m x plus alpha over m

T a n g e n t space p a s s e s space t h r o u g h left parenthesis alpha comma beta right parenthesis space i s space beta equals m alpha plus space 1 divided by space m

alpha m squared minus beta m plus 1 divided by m equals 0

m subscript 1 equals m comma space m subscript 2 equals 2 m
m plus 2 m equals beta over alpha
m equals fraction numerator beta over denominator 3 alpha end fraction
2 m x m equals 1 divided by alpha
2 open parentheses fraction numerator beta squared over denominator 3 alpha end fraction close parentheses equals 1 divided by alpha
beta equals 3 square root of alpha over 2 end root
alpha equals fraction numerator 2 beta squared over denominator 9 end fraction

    Therefore, alpha = fraction numerator 2 over denominator 9 end fraction blank beta 2.

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