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楼主: manthanein

[原创] 欣赏一些函数图象

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 楼主| 发表于 2021-10-6 00:48:05 | 显示全部楼层
\(\D y=\frac{1}{x\sqrt{a^{2}-x^{2}}}\)
https://www.desmos.com/calculator/rs1lv3nmg5
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:49:04 | 显示全部楼层
\(\D y=\frac{1}{x^{2}\sqrt{a^{2}-x^{2}}}\)

https://www.desmos.com/calculator/ixq31zz0yz
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:50:44 | 显示全部楼层
本帖最后由 manthanein 于 2021-10-6 01:31 编辑



\(y=\sqrt{a^{2}-x^{2}} \implies x^2+y^2=a^2\)

https://www.desmos.com/calculator/kmzlansngs

\(y=\sqrt{\left(x-a\right)\left(b-x\right)}\)
\(\implies y^2=(x-a)(b-x)\)
\(\implies y^2=bx-ab-x^2+ax\)
\(\implies x^2+y^2=ax+bx-ab\)
\(\implies \D (x^2-ax-bx)+y^2=-ab\)
\(\implies \D x^2-ax-bx+\frac{(a+b)^2}{4}+y^2=-ab+\frac{(a+b)^2}{4}\)
\(\implies \D (x-\frac{a+b}{2})^2+y^2=\frac{(a-b)^2}{4}\)
https://www.desmos.com/calculator/oydmtjemfb
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:51:56 | 显示全部楼层
\(\D y=\sqrt{\left(a^{2}-x^{2}\right)^{3}}\)

https://www.desmos.com/calculator/9h2x6gdnaq
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:53:16 | 显示全部楼层
\(\D y=x\sqrt{a^{2}-x^{2}}\)

https://www.desmos.com/calculator/sgq6fc58tk
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:54:32 | 显示全部楼层
\(\D y=x^{2}\sqrt{a^{2}-x^{2}}\)

https://www.desmos.com/calculator/54wpr90xls
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:55:25 | 显示全部楼层
\(\D y=\frac{\sqrt{a^{2}-x^{2}}}{x}\)
https://www.desmos.com/calculator/6b0crhtxn0
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:56:44 | 显示全部楼层
\(\D y=\frac{\sqrt{a^{2}-x^{2}}}{x^{2}}\)

https://www.desmos.com/calculator/oc9wkgioie
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 00:58:21 | 显示全部楼层
\(\D y=\frac{1}{\sqrt{ax^{2}+bx+c}}\)

https://www.desmos.com/calculator/7sews9k41d
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2021-10-6 01:03:42 | 显示全部楼层
本帖最后由 manthanein 于 2021-10-6 01:09 编辑

椭圆/双曲线

\(y=\sqrt{ax^{2}+bx+c}\)
\(\implies ax^{2}+bx+c=y^{2}\)
\(\implies 4a^2x^{2}+4abx+4ac=4ay^{2}\)
\(\implies (2ax+b)^2+(4ac-b^2)=4ay^{2}\)
\(\implies \D (x+\frac{b}{2a})^2+\frac{4ac-b^2}{4a^2}=\frac{y^{2}}{a}\)

https://www.desmos.com/calculator/h7g6yiwu26
https://www.desmos.com/calculator/ubeqqvalsx
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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