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Answer: \(45^\circ\) \(\left(\dfrac{\pi}{4}\right)\)

Comparing with \(ax^2+2hxy+by^2=0\): \(a=0\), \(h=\dfrac12\), \(b=1\).

\(\tan\theta=\left|\dfrac{2\sqrt{h^2-ab}}{a+b}\right|=\left|\dfrac{2\sqrt{\frac14-0}}{0+1}\right|=1\), so \(\theta=45^\circ\).

(Check: \(y(x+y)=0\) gives the lines \(y=0\) and \(y=-x\), which make an acute angle of \(45^\circ\).)

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report
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