text: # ASSIGNMENT 9 for SECTION 001
  
  ```ASSIGNMENT 9 for SECTION 001
  This assignment is to be handed in. There are two parts: Part A and Part B.
  Part A will be graded for completeness. You will receive full marks only if every question has been completed.
  and your reasoning is clear. In both parts, you must show your work.
  Please submit Part A and Part B separately, with your name on each part.
  Part A
  From Calculus: Early Transcendentals:
  From section 3.5, complete questions: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32(a) and 32(b),
  34, 36, 40, 60, 62
  Part B
  1. Consider the curve x2 + y 2
  3
  = 8x2 y 2 . Find the equation of the tangent line at the point (−1, 1).
  2. Let P be a point on a curve, and l be the tangent line at P . The normal line at P is the line perpendicular
  to l and passing through P . Consider the curve x2 + (y − x)3 = 9. Find the equation of the normal line
  at x = 1.
  y
  3. The curve
  x2 − xy + y 2 = 3
  describes a tilted ellipse, pictured to the right. Find the area of the
  smallest box (with sides parallel to the axes) containing this ellipse.
  x
  4. A (non-tilted) ellipse centred on the origin is described by the equation
  x2
  y2
  + 2 = 1.
  2
  a
  b
  (2a and 2b are the “width” and “height” of the ellipse.) Prove that if the normal line at every point on
  the ellipse passes through the origin, then the ellipse is a circle.
  5. Describe, in the form of a haiku, how calculus has changed your life.
  ```
explanation: The document is an assignment for a calculus course, specifically for Section 001. It contains two parts: Part A and Part B. Part A lists specific questions from a textbook section, and Part B contains five distinct math questions. The document does not provide answers to these questions.
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: # ASSIGNMENT 9 for SECTION 001
  
  ```ASSIGNMENT 9 for SECTION 001
  This assignment is to be handed in. There are two parts: Part A and Part B.
  Part A will be graded for completeness. You will receive full marks only if every question has been completed.
  and your reasoning is clear. In both parts, you must show your work.
  Please submit Part A and Part B separately, with your name on each part.
  Part A
  From Calculus: Early Transcendentals:
  From section 3.5, complete questions: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32(a) and 32(b),
  34, 36, 40, 60, 62
  Part B
  1. Consider the curve x2 + y 2
  3
  = 8x2 y 2 . Find the equation of the tangent line at the point (−1, 1).
  2. Let P be a point on a curve, and l be the tangent line at P . The normal line at P is the line perpendicular
  to l and passing through P . Consider the curve x2 + (y − x)3 = 9. Find the equation of the normal line
  at x = 1.
  y
  3. The curve
  x2 − xy + y 2 = 3
  describes a tilted ellipse, pictured to the right. Find the area of the
  smallest box (with sides parallel to the axes) containing this ellipse.
  x
  4. A (non-tilted) ellipse centred on the origin is described by the equation
  x2
  y2
  + 2 = 1.
  2
  a
  b
  (2a and 2b are the “width” and “height” of the ellipse.) Prove that if the normal line at every point on
  the ellipse passes through the origin, then the ellipse is a circle.
  5. Describe, in the form of a haiku, how calculus has changed your life.
  ```
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is an assignment for a calculus course, specifically for Section 001. It contains two parts: Part A and Part B. Part A lists specific questions from a textbook section, and Part B contains five distinct math questions. The document does not provide answers to these questions.
  
  Label: multiple-question