If is the chord of contact of the hyperbola , then the equation of the corresponding pair of tangents is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: B
Solution
The chord of contact from an external point (h, k) to x² - y² = 9 is hx - ky = 9. Since the chord of contact is x = 9, we compare: h/1 = k/0 = 9/9, giving h = 1, k = 0. So the external point is (1, 0).
The pair of tangents from (1, 0) to x² - y² = 9 is given by SS₁ = T², where:
- S = x² - y² - 9
- S₁ = 1² - 0² - 9 = -8
- T = x(1) - y(0) - 9 = x - 9
So: (x² - y² - 9)(-8) = (x - 9)²
-8x² + 8y² + 72 = x² - 18x + 81
Rearranging: 9x² - 8y² - 18x + 9 = 0
The pair of tangents from (1, 0) to x² - y² = 9 is given by SS₁ = T², where:
- S = x² - y² - 9
- S₁ = 1² - 0² - 9 = -8
- T = x(1) - y(0) - 9 = x - 9
So: (x² - y² - 9)(-8) = (x - 9)²
-8x² + 8y² + 72 = x² - 18x + 81
Rearranging: 9x² - 8y² - 18x + 9 = 0
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