Question

The image of the pair of lines represented by $a{x}^2+2hxy+b{y}^2=0$ by the line mirror $y=0$ is

• A. $a{x}^2-2hxy+b{y}^2=0$
• B. $b{x}^2-2hxy+a{y}^2=0$
• C. $b{x}^2+2hxy+a{y}^2=0$
• D. $a{x}^2-2hxy-b{y}^2=0$

Answer 1

Answer: (A)

$a{x}^2-2hxy+b{y}^2=0$

We get image of $a{x}^2+2hxy+b{y}^2=0$ by the line $y=0$ by replacing $x\to -x$

$\Rightarrow a{(-x)}^2+2h(-x)y+b{y}^2=0$

$\Rightarrow a{x}^2-2hxy+b{y}^2=0$