text: ## Calculus (3rd Edition)
  
  $$3x^2 -2x +4y^2=1.$$
  We have $$r=\frac{1}{2-\cos\theta}\Longrightarrow 2r-r\cos\theta =1.$$ Recall that $r\cos \theta=x$ and $r^2=x^2+y^2$: Hence, we get $$2\sqrt{x^2+y^2}-x =1\Longrightarrow 4(x^2+y^2)=(1+x)^2=1+2x+x^2.$$ Finally, we get $$3x^2 -2x +4y^2=1.$$
explanation: The text extract is from a Calculus textbook and contains a mathematical derivation. It starts with an equation and proceeds to transform it step-by-step, ultimately arriving at the same equation. The extract does not contain a question or an answer to a question.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## Calculus (3rd Edition)
  
  $$3x^2 -2x +4y^2=1.$$
  We have $$r=\frac{1}{2-\cos\theta}\Longrightarrow 2r-r\cos\theta =1.$$ Recall that $r\cos \theta=x$ and $r^2=x^2+y^2$: Hence, we get $$2\sqrt{x^2+y^2}-x =1\Longrightarrow 4(x^2+y^2)=(1+x)^2=1+2x+x^2.$$ Finally, we get $$3x^2 -2x +4y^2=1.$$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract is from a Calculus textbook and contains a mathematical derivation. It starts with an equation and proceeds to transform it step-by-step, ultimately arriving at the same equation. The extract does not contain a question or an answer to a question.
  
  Label: no-question