Q22 / 40 · NTA Abhyas (JEE Main) 2020 · Mathematics · Hyperbola

The chords passing through 2,1 intersect the hyperbola x216-y29=1 at A and B. The locus of the point of intersection of tangents at A and B on the hyperbola is

  • A
    x-y=1
  • B
    x+y=3
  • Correct answer
    C
    9x-8y=72
  • D
    9x+8y=7

Solution

Let, the point of intersection of the tangents at A & B is h,k.
Then, the equation of AB is xh16-yk9=1 { ∵T=0 is the chord of contact}
Now, xh16-yk9=1 passes through 2,1
Hence, 2h16-k9=1
⇒9h-8k=72
⇒ the locus is 9x-8y=72

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

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