NTA Abhyas JEE Main2020MathematicsHyperbolaPractice

The chords passing through 2,1 intersect the hyperbola x 2 16 - y 2 9 = 1 at A and B . The locus of the point of intersection of tangents at A and B on the hyperbola is

Options

Ax - y = 1
Bx + y = 3
C9 x - 8 y = 72
D9 x + 8 y = 7

Correct answer

C. 9 x - 8 y = 72

Step-by-step solution

Let, the point of intersection of the tangents at A & B is h , k . Then, the equation of A B is x h 16 - y k 9 = 1 ∵ T = 0 is the chord of contact Now, x h 16 - y k 9 = 1 passes through 2,1 Hence, 2 h 16 - k 9 = 1 ⇒ 9 h - 8 k = 7 2 ⇒ the locus is 9 x - 8 y = 72

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