Question

If the line ax + by + c = 0 is normal to the curve x y + 5 = 0 then

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

Answer 1

Answer: (C)

a < 0, b < 0

Answer 2

x y = -5 ⇒ x $\frac{dy}{dx}$+ y = 0 ⇒ $\frac{dy}{dx}$= –$\frac{y}{x}$> 0

(as xy = - 5 < 0)

⇒ The Slope of the normal is negative ⇒ –$\frac{a}{b}$< 0 ⇒$\frac{a}{b}$> 0

⇒ a > 0 , b > 0 or a < 0 , b < 0