# 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
2 years, 7 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Wow nice! You should put them in the wiki here!

- 2 years, 7 months ago