Question

X²+2 x y+y²+x-y=0 Use a rotation of axes to eliminate the x y -term.

Answer 1

To eliminate the xy-term in the equation x²+2xy+y²+x-y=0, you can use a rotation of axes.

Step-by-step explanation:

To eliminate the xy-term in the equation x²+2xy+y²+x-y=0, we can use a rotation of axes. Let's assume the new variables u and v, where x = ucosθ - vsinθ and y = usinθ + vcosθ. Plugging these values into the given equation, we get:

(ucosθ - vsinθ)² + 2(ucosθ - vsinθ)(usinθ + vcosθ) + (usinθ + vcosθ)² + (ucosθ - vsinθ) - (usinθ + vcosθ) = 0

This equation can then be simplified further to eliminate the xy-term.