Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. 5x2 – 6xy + 5y2 – 12 = 0

Question

i need an answer for this ASAP

Answer 1

5x²-6xy+5y²=12  Note that this eq. is symmetric in x and y which means it's symmetric to the line y=x, so look at it in an x'y'-coordinate system rotated by 45°.

(Let θ=45^° in the transformation matrix R, for X=RX')

 

Substitute x=(1/√2)(x'-y'), y=(1/√2)(x'+y') and get

x'²+4y'²=6

Answer 2

1) cos (2θ) = (A - C) / B, or (5 - 5) / -6, or 0. θ = 0.

2) determine sin 0 and cos 0

3) substitute sin 0 and cos 0 into

       x = x'cos 0 - y'sin 0

       y = x'sin 0 - y'cos 0

4) substitute for x and y in original equation, simplify

5) convert to standard form.