Question

If the line ax + by + c = 0 is a tangent to the curve xy = 4, then

• A. a > 0, b > 0
• B. a > 0, b < 0
• C. a < 0, b > 0
• D. None of these

Answer 1

Answer: (A)

a > 0, b > 0

Answer 2

We have xy = 4 Ž y = $\frac{4}{x}$ Ž$\frac{dy}{dx}$

= – $\frac{4}{x^{2}}$slope of tangent,

slope of line Ž ax + by + c = 0 is – $\frac{a}{b}$

Since line is tangent to the curve

Ž –$\frac{4}{x^{2}}$= –$\frac{a}{b}$Ž $\frac{a}{b}$= +ve

Ž possible if a > 0, b > 0 and a < 0, b < 0