MHT CET2012MathematicsParabola

The intercept of the latusrectum to the parabola y²=4 a x are b and k , then k is equal to

Options

Aa b a-b
Ba b-a
Cb b-a
Da b b-a

Correct answer

D. a b b-a

Step-by-step solution

For latusrectum P Q . y (t₁+t₂ )-2 x-2 a t₁ t₂=0 and t₁ t₂=-1 For any point P(x, y) , the focal distance is a+x . b=a+x=a+a t₁²=a (1+t₁² ) ( i )c=a+x=a+a t₂²=a+ a t₁² ( t₁ t₂=-1 )= a (1+t₁² ) t₁² ...(ii) b c =t₁² From Eq. (i), b=a (1+ b c ) b=a+ a b c c= a b b-a

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