Question

The differential equation \( (3x + 4y + 1) dx + (4x + 5y + 1) dy = 0 \) represents a family of

• A. circles
• B. parabolas
• C. ellipses
• D. hyperbolas

Hint:

Differential equations involving quadratic forms in \( x \) and \( y \) can represent conic sections, such as hyperbolas.

Answer 1

The Correct Option is D

By comparing the equation with the standard form of a hyperbola equation, we deduce that it represents a family of hyperbolas.