fracx^236+fracy^29 = 1

Frequently Asked Questions

• 找到椭圆的中心 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

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

• 找到椭圆的焦点 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$F_1=\left(-3\sqrt{3},0\right),F_2=\left(3\sqrt{3},0\right)$$

• 找到椭圆的顶点 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$V_1=\left(0,3\right),V_2=\left(0,-3\right),V_3=\left(6,0\right),V_4=\left(-6,0\right)$$

• 求椭圆的离心率 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$e=\frac{\sqrt{3}}{2}$$

• $$\text{求解 }x$$ \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\begin{array}{rl}& x=2\sqrt{9-y^2}\\ & x=-2\sqrt{9-y^2}\end{array}$$

• $$\text{求解 }y$$ \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\begin{array}{rl}& y=\frac{\sqrt{36-x^2}}{2}\\ & y=-\frac{\sqrt{36-x^2}}{2}\end{array}$$

• 测试关于原点的对称性 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\text{Symmetry with respect to the origin}$$

• 测试关于 x 轴的对称性 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\text{Symmetry with respect to the x-axis}$$

• 测试关于 y 轴的对称性 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\text{Symmetry with respect to the y-axis}$$

• $$\text{求关于 }x\text{ 的导数}$$ \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\frac{dy}{dx}=-\frac{x}{4y}$$

• $$\text{求关于 }y\text{ 的导数}$$ \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\frac{dx}{dy}=-\frac{4y}{x}$$

• $$\text{求出关于 }x\text{ 的二阶导数}$$ \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\frac{d^{2}y}{d{x}^2}=-\frac{4y^2+x^2}{16y^3}$$

• $$\text{求出关于 }y\text{ 的二阶导数}$$ \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\frac{d^{2}x}{d{y}^2}=-\frac{4x^2+16y^2}{x^3}$$

• 以极坐标形式重写 \(\frac{x^2}{36}+\frac{y^2}{9} = 1\)

  

  $$\begin{array}{rl}& r=\frac{6\sqrt{1+3{\sin }^2\left(\theta \right)}}{1+3{\sin }^2\left(\theta \right)}\\ & r=-\frac{6\sqrt{1+3{\sin }^2\left(\theta \right)}}{1+3{\sin }^2\left(\theta \right)}\end{array}$$