x^2 + y^2 = 1

Frequently Asked Questions

• Find the radius of the circle of \(x^{2} + y^{2} = 1\)

  

  $$r=1$$

• Find the center of the circle of \(x^{2} + y^{2} = 1\)

  

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

• $$\text{Solve for }x$$ of \(x^{2} + y^{2} = 1\)

  

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

• $$\text{Solve for }y$$ of \(x^{2} + y^{2} = 1\)

  

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

• Testing for symmetry about the origin of \(x^{2} + y^{2} = 1\)

  

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

• Testing for symmetry about the x-axis of \(x^{2} + y^{2} = 1\)

  

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

• Testing for symmetry about the y-axis of \(x^{2} + y^{2} = 1\)

  

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

• $$\text{Find the derivative with respect to }x$$ of \(x^{2} + y^{2} = 1\)

  

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

• $$\text{Find the derivative with respect to }y$$ of \(x^{2} + y^{2} = 1\)

  

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

• $$\text{Find the second derivative with respect to }x$$ of \(x^{2} + y^{2} = 1\)

  

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

• $$\text{Find the second derivative with respect to }y$$ of \(x^{2} + y^{2} = 1\)

  

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

• Rewrite in polar form of \(x^{2} + y^{2} = 1\)

  

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