The equation of common tangent to the curve y² = 8x and xy = - 1 is

Solution:

Let the common tangent be: $$y = mx + c$$ For curve \( y^2 = 8x \):
Condition for tangency gives: $$mc = 2 \quad \text{(1)}$$ For curve \( xy = -1 \):
Condition for tangency gives: $$c^2 = 4m \quad \text{(2)}$$ Substitute \( c = \frac{2}{m} \) from (1) into (2): $$\left(\frac{2}{m}\right)^2 = 4m \Rightarrow \frac{4}{m^2} = 4m \Rightarrow m^3 = 1 \Rightarrow m = 1$$ Then, \( c = \frac{2}{1} = 2 \)

Final Answer:
$$\boxed{y = x + 2}$$