Question

Question(6)
If the new equation of xy = 0 is x2 - y2 = 0,the angle of rotation of axes is
B
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Answer 1

Answer:

45° or 2nπ+(π/4)

Step-by-step explanation:

from old equation:

X=0 and Y=0

from new equation:

X=Y and X=-Y

slope of X=Y is 45° and slope of X=-Y is 135°

thus rotational angle is 45° and new co ordinate are X+Y/√2 and Y-X/√2 thus new equation is

>>>(X+Y/√2 )×(Y-X/√2)=0

>>>Y^2-X^2/2=0

>>>Y^2-X^2=0

taking negative sign common, we get

x2 - y2 = 0 which proves that rotational angle is 45°

Answer 2

The angle of rotation of axes is θ = Π / 4

Given:

xy = 0

and $x^{2}$ - y2 = 0

To Find:

The angle of rotation of the axes from the given

Solution:

xy= 0 .............(1)

x = Xcosθ - Ysinθ

y = Xsinθ + Ysinθ

substitute in eqn(1)

We have,

[ Xcosθ - Ysinθ][Xsinθ + Ysinθ] = 0

Upon solving we get ,

X2 - Y2 =0

So,

0 + XY{cos2θ} = 0

The angle of rotation of axes isθ = Π/4

#SPJ3