Science:Math Exam Resources/Courses/MATH105/April 2015/Question 01 (b)
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Question 01 (b) 

Are the level curves of the paraboloid lines, circles, parabolas, hyperbolas or ellipses? 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Level curves of a function can be visualized by setting to some constant and sketching the result. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Notice that must be a nonnegative number for any . By setting to be some constant we have
This equation represents circles of radius (centered at the origin). Therefore, the level curves of the paraboloid are 