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: (B)

9x² – 8y² – 18x + 9 = 0

Answer 2

If x = 9 meets the hyperbola x² – y² = 9 at (9, 6$\sqrt{2}$) and (9, –6$\sqrt{2}$). The equations of the tangents to the hyperbola at these points are

3x – 2$\sqrt{2}$y – 3 = 0 and 3x + 2$\sqrt{2}$y – 3 = 0

Joint equation of the two tangents is therefore

(3x – 2$\sqrt{2}$y – 3) (3x + 2$\sqrt{2}$y – 3) = 0

Ž (3x – 3)² – (2$\sqrt{2}$y)² = 0 Ž 9x² – 8y² – 18x + 9 = 0.