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# A few properties for solving eclipse problems

For an eclipse centered at the origin $$\dfrac { {x }^{ 2} }{ { a }^{ 2} } +\dfrac { {y }^{ 2} }{ { b}^{ 2} } =1$$:

1. Any point $$P$$ on the eclipse can be expressed as $$(a\cos\theta ,b\sin\theta )$$ (or $$(a\sin\theta ,b\cos\theta )$$);

2. Equation of the line tangent to the eclipse through point P is $$\dfrac {x\cos\theta }{a } +\dfrac {y\sin\theta }{b } =1$$;

3. The distance from the origin to the line $$ax + by = c$$ is $$\left|\dfrac { c }{ \sqrt { { a }^{2 }+{ b }^{ 2 } } } \right|$$;

Note by Minjie Lei
1 year, 7 months ago

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