x^2 + y^2 + x = 0

Frequently Asked Questions

• Find the standard equation of the circle of $x^2+y^2+x=0$

  

  $${\left(x+\frac{1}{2}\right)}^2+y^2=\frac{1}{4}$$

• Find the radius of the circle of $x^2+y^2+x=0$

  

  $$r=\frac{1}{2}$$

• Find the center of the circle of $x^2+y^2+x=0$

  

  $$\left(-\frac{1}{2},0\right)$$

• $\text{Solve for }x$ of $x^2+y^2+x=0$

  

  $$\begin{array}{rl}& x=\frac{-1+\sqrt{1-4y^2}}{2}\\ & x=-\frac{1+\sqrt{1-4y^2}}{2}\end{array}$$

• $\text{Solve for }y$ of $x^2+y^2+x=0$

  

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

• Testing for symmetry about the origin of $x^2+y^2+x=0$

  

  $$\text{Not symmetry with respect to the origin}$$

• Testing for symmetry about the x-axis of $x^2+y^2+x=0$

  

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

• Testing for symmetry about the y-axis of $x^2+y^2+x=0$

  

  $$\text{Not symmetry with respect to the y-axis}$$

• $\text{Find the derivative with respect to }x$ of $x^2+y^2+x=0$

  

  $$\frac{dy}{dx}=-\frac{2x+1}{2y}$$

• $\text{Find the derivative with respect to }y$ of $x^2+y^2+x=0$

  

  $$\frac{dx}{dy}=-\frac{2y}{2x+1}$$

• $\text{Find the second derivative with respect to }x$ of $x^2+y^2+x=0$

  

  $$\frac{d^{2}y}{d{x}^2}=-\frac{4y^2+4x^2+4x+1}{4y^3}$$

• $\text{Find the second derivative with respect to }y$ of $x^2+y^2+x=0$

  

  $$\frac{d^{2}x}{d{y}^2}=-\frac{8x^2+8x+2+8y^2}{8x^3+12x^2+6x+1}$$

• Rewrite in polar form of $x^2+y^2+x=0$

  

  $$\begin{array}{rl}& r=0\\ & r=-\cos \left(\theta \right)\end{array}$$