Question

The equation of the common tangent 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

Any point on y² = 8x is (2t², 4t) where the tangent is

yt = x+2t².

Solving it with xy = -1, y(yt – 2t²) =-1 or ty² – 2t²y + 1 = 0.

For common tangent, it should have equal roots.

∴ 4t⁴ – 4t = 0 ⇒ t = 0, 1

∴ The common tangent is y = x+2, (when t = 0, it is x =0 which can touch xy = -1 at infinity only)