\(\D y=\frac{1}{x\sqrt{a^{2}-x^{2}}}\)
https://www.desmos.com/calculator/rs1lv3nmg5
\(\D y=\frac{1}{x^{2}\sqrt{a^{2}-x^{2}}}\)
https://www.desmos.com/calculator/ixq31zz0yz
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
\(\D y=\sqrt{\left(a^{2}-x^{2}\right)^{3}}\)
https://www.desmos.com/calculator/9h2x6gdnaq
\(\D y=x\sqrt{a^{2}-x^{2}}\)
https://www.desmos.com/calculator/sgq6fc58tk
\(\D y=x^{2}\sqrt{a^{2}-x^{2}}\)
https://www.desmos.com/calculator/54wpr90xls
\(\D y=\frac{\sqrt{a^{2}-x^{2}}}{x}\)
https://www.desmos.com/calculator/6b0crhtxn0
\(\D y=\frac{\sqrt{a^{2}-x^{2}}}{x^{2}}\)
https://www.desmos.com/calculator/oc9wkgioie
\(\D y=\frac{1}{\sqrt{ax^{2}+bx+c}}\)
https://www.desmos.com/calculator/7sews9k41d
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