Question

The transformed equation of 2xy + a^2 =0 when the axes are rotated through an angle π/4 is

Answer 1

The required equation is

$X^2-Y^2+a^2=0$

Step-by-step explanation:

Given equation is

$2xy +a^2=0$

Since the axes are rotated though an angle $\frac{\pi}{4}$, then

$x=Xcos 45^\circ -Ysin 45 ^\circ=\frac{1}{\sqrt{2} } (X-Y)$    and

$y=X sin 45^\circ+Ycos45^\circ=\frac{1}{\sqrt{2} } (X+Y)$

Putting the value of x and y in the given equation,

$2.\frac{1}{\sqrt{2} }(X-Y) .\frac{1}{\sqrt{2} }.(X+Y) +a^2=0$

$\Leftrightarrow X^2-Y^2+a^2=0$

The required equation is

$X^2-Y^2+a^2=0$

Answer 2

Step-by-step explanation:

The transformed equation of 2xy+a2=0 when the axes are rotated through an angle π/4 is?