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

General equation of tangent to the curve y² = 8x is

y = mx + 2/m.

Now on solving it with xy = 1, put discri - minant = 0.

$x\left( mx + \frac{2}{m} \right) = - 1 \Rightarrow m = 1$