Question

The lines represented by the equation $9x^2+24xy+16y^2+21x+28y+6=0$ are

• A. Parallel
• B. Coincident
• C. Perpendicular
• D. None of these

Answer 1

The correct option is A

Parallel

Find the nature of the family of lines

Given, $9x^2+24xy+16y^2+21x+28y+6=0$

Comparing with the general equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$

We get,

$$\begin{gathered} a=9 \\ h=12 \\ b=16 \end{gathered}$$

Now,

$\Rightarrow h^2-ab=144-(16\times 9)=0$

So, the given lines are parallel.

Hence, option $A$ is correct answer.