text: ## Question
  
  ### Solution
  
  Correct option is
  
  #### SIMILAR QUESTIONS
  
  Q1
  
  Find the equation of diameter of the circle x2 + y2 + 2gx + 2fy + c = 0 which corresponds o the chord ax + by + λ = 0.
  
  Q2
  
  Examine if the two circle x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally. Also the pointed contact.
  
  Q3
  
  Find the equation of the circle passing through (1, 1) and the point of intersection of circles.
  
  x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0
  
  Q4
  
  Find the equation of circle passing through the point of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 and whose centre lies on the line y = x.
  
  Q5
  
  Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y – 40 = 0.
  
  Q6
  
  Find the equation of circle through points of intersection of circle x2 + y2– 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x + 2y = 0.
  
  Q7
  
  Find the angle between the circles. S = x2 + y2 – 4x + 6y + 11 = 0 and
  
  Q8
  
  Find the equation of the system of circles coaxial with the circles.
  
  x2 + y2 + 4x + 2y + 1 = 0, x2 + y2 – 2x + 6y – 6 = 0
  
  Also find the equation of that particular circle whose centre lies on radical axis.
  
  Q9
  
  Find the locus of pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.
  
  Q10
  
  Find the equation of circle which cuts the circle x2 + y2 + 5x + 7y + 4 = 0 orthogonally, has its centre on the line x = 2, and passes through the point (4, –1).
explanation: The provided text is a series of questions and solutions related to the topic of circles in coordinate geometry. Each section contains a question followed by a solution. The questions involve finding equations of circles, determining the nature of their intersections, and other geometric properties.
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: ## Question
  
  ### Solution
  
  Correct option is
  
  #### SIMILAR QUESTIONS
  
  Q1
  
  Find the equation of diameter of the circle x2 + y2 + 2gx + 2fy + c = 0 which corresponds o the chord ax + by + λ = 0.
  
  Q2
  
  Examine if the two circle x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally. Also the pointed contact.
  
  Q3
  
  Find the equation of the circle passing through (1, 1) and the point of intersection of circles.
  
  x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0
  
  Q4
  
  Find the equation of circle passing through the point of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 and whose centre lies on the line y = x.
  
  Q5
  
  Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y – 40 = 0.
  
  Q6
  
  Find the equation of circle through points of intersection of circle x2 + y2– 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x + 2y = 0.
  
  Q7
  
  Find the angle between the circles. S = x2 + y2 – 4x + 6y + 11 = 0 and
  
  Q8
  
  Find the equation of the system of circles coaxial with the circles.
  
  x2 + y2 + 4x + 2y + 1 = 0, x2 + y2 – 2x + 6y – 6 = 0
  
  Also find the equation of that particular circle whose centre lies on radical axis.
  
  Q9
  
  Find the locus of pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.
  
  Q10
  
  Find the equation of circle which cuts the circle x2 + y2 + 5x + 7y + 4 = 0 orthogonally, has its centre on the line x = 2, and passes through the point (4, –1).
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a series of questions and solutions related to the topic of circles in coordinate geometry. Each section contains a question followed by a solution. The questions involve finding equations of circles, determining the nature of their intersections, and other geometric properties.
  
  Label: multiple-question-and-answer