Q27 / 92 · NTA Abhyas (JEE Main) 2020 · Mathematics · Parabola

The locus of mid-points of all chords of parabola y2=4x, for which all circles drawn taking them as diameters passes through the vertex of the parabola is a conic whose length of the smallest focal chord is equal to

  • A
    1 units
  • Correct answer
    B
    2 units
  • C
    3 units
  • D
    4 units

Solution

Figure

Circle drawn by taking AB as diameter passes through vertex hence AV is perpendicular to BV

Let h,k be the mid-point of the chord
⇒t1t2=-4, h=t12+t222, k=2t1+t22
k2=t12+t22+2t1t2
⇒y2=2x-8

Hence, the locus of the conic is y2=2x-4
⇒ Length of the latus rectum (smallest focal chord) =2 units

Hence, the correct answer is option: 'B'.

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