Question

The tangents to the hyperbola drawn from the point (a, b) are inclined at angles ‘q’ and ‘f’ to the x axis. If tanq. tanf = 2 and hyperbola is 3x² – 2y² = 6. Then

• A. b² = a² – 1
• B. b² = 2a² – 7
• C. 2b² = a² – 1
• D. 2b² + a² = 2

Answer 1

Answer: (B)

b² = 2a² – 7

Answer 2

S = 3x² – 2y² – 6 = 0

joint equation of tangents SS₁ = T²

pair of tangents (3x² – 2y² – 6) (3a² – 2b² – 6)
= (3ax – 2by – 6)²

product of slope of the lines = $\frac{Coeff.ofx^{2}}{Coeff.ofy^{2}}$

i.e. tanq tanf = $\frac{3(3\alpha^{2} - 2\beta^{2} - 6) - 9\alpha^{2}}{2(3\alpha^{2} - 2\beta^{2} - 6) - 4\beta^{2}}$

2 = $\frac{- 6\beta^{2} - 18}{- 6\alpha^{2} + 12}$ Ž b² = 2a² – 7