Question

The equation $x^2+4xy+4y^2-3x-6y-4=0$ represents a

• A. circle
• B. parabola
• C. a pair of lines
• D. none of these

Answer 1

The correct option is C a pair of lines

Here, $a=1,b=4,c=-4,,h=2,f=-3,g=-\frac{3}{2}$
Now, $\Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2$

$\Delta =\left(1\right)\left(4\right)(-4)+2(-3)(-\frac{3}{2})\left(2\right)-\left(1\right)(-3{)}^2-(4\left)\right(-\frac{3}{2}{)}^2-(-4)(2{)}^2$

$=-16+18-9-9+16$

$=0$
Also, $h^2=ab$
Hence, given equation represents a pair of straight lines.