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Most Important Selected Qs for JEE AdvancedMathematicsParabola

If two distinct chords of a parabola x^2=4 ay passing through (2 a, a) are bisected on the line x+y=1 , then length of latus rectum can be -

Options

  1. A2
  2. B1
  3. C4
  4. D5

Correct answer

B. 1

Step-by-step solution

Any point on the line x+y=1 can be taken as ( , 1- ) so equation of the chord taking this point as mid point will be x-2(y+1- )= ^2-4 a(1- ) It passes through (2 a, a) aligned & 2 a -2 a ( a +1- )= ^2-4 a (1- ) & ^2-2 a +2 a ^2=0 aligned It has two distinct root then aligned & - (-2 a +2 a ^2 ) 0 & a ^2- a 0 0 a 1 aligned length of latus rectum can be between 0 and 4 .

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