გადაწყვიტეთ x^2/a^2+y^2/b^2=1

$$\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$$

ამოხსნა a-ისთვის (complex solution)

$$\left\{\begin{matrix}a=-i\left(y^{2}-b^{2}\right)^{-\frac{1}{2}}bx\text{; }a=i\left(y^{2}-b^{2}\right)^{-\frac{1}{2}}bx\text{, }&x\neq 0\text{ and }b\neq 0\text{ and }y\neq -b\text{ and }y\neq b\\a\neq 0\text{, }&\left(y=-b\text{ or }y=b\right)\text{ and }x=0\text{ and }b\neq 0\end{matrix}\right.$$

ამოხსნა b-ისთვის (complex solution)

$$\left\{\begin{matrix}b=-i\left(x^{2}-a^{2}\right)^{-\frac{1}{2}}ay\text{; }b=i\left(x^{2}-a^{2}\right)^{-\frac{1}{2}}ay\text{, }&a\neq 0\text{ and }y\neq 0\text{ and }x\neq -a\text{ and }x\neq a\\b\neq 0\text{, }&\left(x=-a\text{ or }x=a\right)\text{ and }y=0\text{ and }a\neq 0\end{matrix}\right.$$

ამოხსნა a-ისთვის

$$\left\{\begin{matrix}a=\sqrt{-\frac{1}{y^{2}-b^{2}}}bx\text{; }a=-\sqrt{-\frac{1}{y^{2}-b^{2}}}bx\text{, }&x\neq 0\text{ and }|y|<|b|\text{ and }b\neq 0\\a\neq 0\text{, }&x=0\text{ and }|y|=|b|\text{ and }b\neq 0\end{matrix}\right.$$

ამოხსნა b-ისთვის

$$\left\{\begin{matrix}b=\sqrt{-\frac{1}{x^{2}-a^{2}}}ay\text{; }b=-\sqrt{-\frac{1}{x^{2}-a^{2}}}ay\text{, }&y\neq 0\text{ and }|x|<|a|\text{ and }a\neq 0\\b\neq 0\text{, }&y=0\text{ and }|x|=|a|\text{ and }a\neq 0\end{matrix}\right.$$