Question

The nature of straight lines represented by the equation $4x^{2} + 12xy + 9y^{2} = 0$ is

• A. Real and coincident
• B. Real and different
• C. Imaginary and different
• D. None of the above

Answer 1

Answer: (A)

Real and coincident

Answer 2

$4x^{2} + 12xy + 9y^{2} = 0$

Here$h^{2} - ab = 36 - 36 = 0$, $\left( \text{from}\tan\theta = \frac{\pm 2\sqrt{h^{2} - ab}}{a + b} \right)$

Hence, lines are real and coincident.