Question

Equation of a common tangents to the curves y² = 8x and

xy = –1 is

• A. 3y = 9x + 2
• B. y = 2x + 1
• C. 2y = x + 8
• D. y = x + 2

Answer 1

Answer: (D)

y = x + 2

Answer 2

Equation of a tangent at (at², 2at) to y² = 8x is

ty = x + at² where 4a = 8 i.e. a = 2

̃ ty = x + 2t² which intersects the curve xy = –1 at the points given by $\frac{x(x + 2t^{2})}{t}$= –1 clearly t ¹ 0 or

x² + 2t²x + t = 0 and will be a tangent to the curve if the roots of this quadratic equation are equal, for which 4t⁴ – 4t = 0

̃ t = 0 or t = 1 and an equation of a common tangent is

y = x + 2.