Question

The differential equation of the family of hyperbolas with asymptotes as the line x + y = 1 and x – y = 1 is:

• A. yy¢ + x = 0
• B. yy¢ = (x –1)
• C. yy¢¢+ y¢= 0
• D. y¢ + xy = 0

Answer 1

Answer: (B)

yy¢ = (x –1)

Answer 2

Solving the equations of the asymptotes the centre is x = 1 and y = 0, since e =$\sqrt{2}$the equation of the family of the hyperbola is

$\frac{(x - 1)^{2}}{a^{2}}$– $\frac{(y)^{2}}{a^{2}}$= 1

Ž 2(x – 1) –2y$\frac{dy}{dx}$= 0

Ž (x – 1) = yy¢ is differential equation