Question

If the line ax + by + c = 0 is a normal to the curve xy = 1, then

(a) a > 0, b > 0

(b) a > 0, b < 0

(c) a < 0, b > 0

(d) a < 0, b < 0

Answer 1

Correct option (b) a > 0, b < 0

Explanation:

Given curve is xy = 1

Let the point be (h, k)

Now, y = 1/x ⇒  dy/dx = – 1/x²

Sople of normal = (dy/dx)(h, k) = h²

Equation of normal at (h, k) is

y – k = h²(x – h)

⇒ h²x – y + (k – h) = 0

Given normal is ax + by + c = 0

Comparing the co-efficients of x and y, we get,

a/h² = b/–1 = c/(k – h)

Thus, a > 0 and b < 0.