Question

toom
To remove the
xy
from the equation.
ax² + zhxy + by ² = 0 the axes should be
rotated through an angle 'o' when is not equal to b.​

Answer 1

Answer:

To remove the xy-term from the equation ax2 + 2hxy + by2 = 0, the axes are to be rotated through the angle (1/2) Tan-1 [2h/(a - b)] when a ≠ b and through the angle π/4 when a = b.

HOPE IT HELPS YOU...

Answer 2

Step-by-step explanation:

Suppose axes are rotated through an angle θ in the anticlockwise sense.

Let x = X cosθ -  Y cos θsin and y = X sin θ + Y sinθ. 

Therefore, the given equation will be transformed to a(X cos θ -  Y sin θ)2 + 2h (X cos θ - Y sinθ)(X sin θ +  Y cos θ) + b(X sinθ +  Y cos θ)2 = 0( cos sin ) In this equation, the coefficient of xy is

Answer in the figure. Hope this will help you.