Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 09 (a)
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 • Q8 (a) • Q8 (b) • Q9 (a) • Q9 (b) • Q9 (c) • Q10 (a) • Q10 (b) • Q10 (c) • Q11 (a) • Q11 (b) • Q11 (c) • Q11 (d) • Q11 (e) • Q12 (a) • Q12 (b) • Q13 (a) • Q13 (b) • Q13 (c) • Q13 (d) •
Question 09 (a) 

The curve is known as a Limaçon of Pascal.
(a) Find the equation of the line tangent to the Limaçon at the point . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Use implicit differentiation. 
Hint 2 

Recall that is considered as a function of . Remember to use the chain rule. 
Hint 3 

The equation of tangent line at the point is given by . 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. According to Hint 1 and Hint 2, we differentiate both sides with respect to using chain rule and power rule: Let . Then, the left hand side of the equation is . Considering as a function of , can be also considered as a function of . Taking to the equation, we have Then, plugging ,
which can be simplified as
This is the slope of the tangent line. Using Hint 3, the equation of the tangent line at is or Answer: the equation of the tangent line at the point is . 