Question

The equation of common tangents to the parabola y² = 8x and hyperbola 3x² – y² = 3, is-

• A. 2x ± y + 1 = 0
• B. 2x ± y – 1 = 0
• C. x ± 2y + 1 = 0
• D. x ± 2y – 1 = 0

Answer 1

Answer: (A)

2x ± y + 1 = 0

Answer 2

Tangent to y² = 8x … (1) is y = mx + $\frac{2}{m}$ …(2)

Tangent to $\frac{x^{2}}{1}$–$\frac{y^{2}}{3}$= 1 ...(3) is

y = mx ±$\sqrt{m^{2} - 3}$…(4)

On comparing the equation (2) and (4)

̃ $\frac{2}{m}$=±$\sqrt{m^{2} - 3}$̃ m = ± 2 ; eqn. (2)

̃ 2x ± y + 1 = 0