Question

Write the equation in terms of a rotated x'y'-system using θ, the angle of rotation. Write the equation involving x' and y' in standard form. xy +16 = 0; θ = 45°

Answer 1

\[x=x' \cos\theta-y'\sin\theta\\
y=x'\sin\theta+y'\cos\theta\]
Since \(\theta=\frac{\pi}{4}\), \(\sin\theta=\cos\theta=\frac{1}{\sqrt{2}}\).
Now, substitute \(x=\frac{1}{\sqrt{2}}(x'-y')\) and \(y=\frac{1}{\sqrt{2}}(x'+y')\) into \(xy+16=0\).

Answer 2

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