x^2 + y^2 = 1

常见问题解答

• 求圆的半径 \(x^{2} + y^{2} = 1\)

  

  $$r=1$$

• 找到圆心 \(x^{2} + y^{2} = 1\)

  

  $$\left(0,0\right)$$

• $$\text{求解 }x$$ \(x^{2} + y^{2} = 1\)

  

  $$\begin{array}{rl}& x=\sqrt{1-y^2}\\ & x=-\sqrt{1-y^2}\end{array}$$

• $$\text{求解 }y$$ \(x^{2} + y^{2} = 1\)

  

  $$\begin{array}{rl}& y=\sqrt{1-x^2}\\ & y=-\sqrt{1-x^2}\end{array}$$

• 测试关于原点的对称性 \(x^{2} + y^{2} = 1\)

  

  $$\text{关于原点对称}$$

• 测试关于 x 轴的对称性 \(x^{2} + y^{2} = 1\)

  

  $$\text{关于x轴对称}$$

• 测试关于 y 轴的对称性 \(x^{2} + y^{2} = 1\)

  

  $$\text{关于y轴对称}$$

• $$\text{求关于 }x\text{ 的导数}$$ \(x^{2} + y^{2} = 1\)

  

  $$\frac{dy}{dx}=-\frac{x}{y}$$

• $$\text{求关于 }y\text{ 的导数}$$ \(x^{2} + y^{2} = 1\)

  

  $$\frac{dx}{dy}=-\frac{y}{x}$$

• $$\text{求出关于 }x\text{ 的二阶导数}$$ \(x^{2} + y^{2} = 1\)

  

  $$\frac{d^{2}y}{d{x}^2}=-\frac{y^2+x^2}{y^3}$$

• $$\text{求出关于 }y\text{ 的二阶导数}$$ \(x^{2} + y^{2} = 1\)

  

  $$\frac{d^{2}x}{d{y}^2}=-\frac{x^2+y^2}{x^3}$$

• 以极坐标形式重写 \(x^{2} + y^{2} = 1\)

  

  $$\begin{array}{rl}& r=1\\ & r=-1\end{array}$$