Question

If x = 9 is the chord of contact of the hyperbola x² - y² = 9, then the equation of the corresponding pair of tangents is

• A. 9x² - 8y² + 18x - 9 = 0
• B. 9x² - 8y² - 18x + 9 = 0
• C. 9x² - 8y² - 18x - 9 = 0
• D. 9x² - 8y² + 18x + 9 = 0

Answer 1

Answer: (C)

9x² - 8y² - 18x - 9 = 0

Answer 2

If chord of contact of tangent meet at (h, k), then its equal is hx - ky - 9 = 0

Comparing it with x = 9, we get point of contact as (1, 0)

Using SS₁ = T², the required equation is

(x² - y² - 9) (1 - 9) = (x - 9)²

⇒ 9x² - 8y² - 18x + 9 = 0.