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# [原创] 欣赏一些函数图象

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

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

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 圆 $$y=\sqrt{a^{2}-x^{2}} \implies x^2+y^2=a^2$$ 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

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

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

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

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

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

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

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

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