# 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.
```
The text passage is an assignment for a calculus course, containing a list of questions from a textbook and additional problems to be solved, including finding equations of tangent and normal lines, and proving properties of ellipses.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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.
```
user
The text passage is an assignment for a calculus course, containing a list of questions from a textbook and additional problems to be solved, including finding equations of tangent and normal lines, and proving properties of ellipses.

TYPE: MULTIPLE_QUESTIONS