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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Hyperbola

NTA Abhyas 2020 · Mathematics · Hyperbola

The chords passing through (2,1) intersect the hyperbola x^ 2 16 -...

The chords passing through (2,1)\left(2,1\right) intersect the hyperbola x216−y29=1\dfrac{x^{2}}{16} - \dfrac{y^{2}}{9} = 1 at AandB.A and B . The locus of the point of intersection of tangents at AandBA and B on the hyperbola is

Options

  1. Ax−y=1x - y = 1
  2. Bx+y=3x + y = 3
  3. C9x−8y=729x - 8y = 72
  4. D9x+8y=79x + 8y = 7

Correct answer

C. 9x−8y=729x - 8y = 72

Step-by-step solution

Let, the point of intersection of the tangents at A&Bis(h,k).<br/>Then,is \left(h, k\right) .<br />Then, the equation ofABisxh16−yk9=1is \dfrac{xh}{16} - \dfrac{yk}{9} =1 { ∵T=0∵ T = 0 is the chord of contact}
Now,~xh16−yk9=\dfrac{xh}{16} - \dfrac{yk}{9} =1passesthrough(2,1)<br/>Hence, 2h16−k9=1passes through \left(2,1\right)<br />Hence,~\dfrac{2h}{16} - \dfrac{k}{9} =1
⇒9h−8k=72⇒ 9h - 8k = 72
⇒⇒~the locus is 9x−8y=729x - 8y = 72
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