Question

If the pair of straight lines $a{x}^2+2hxy+b{y}^2=0$ is rotated about the origin through ${90}^{\circ },$ then the equations in the new position is

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

Answer 1

The correct option is D $b{x}^2-2hxy+a{y}^2=0$

When the axes rotated about $90°$
$x=Y$ and $y=-X$
hence putting the respective values in the above equation, we get
$b{X}^2-2hXY+a{Y}^2=0$
hence the equation will be
$b{x}^2-2hxy+a{y}^2=0$