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How do you sketch (x^2-5)^2+y^2=16 without a calculator or software?

  • Thread starter GravitySK
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  • #1
5
1

Homework Statement:

curve sketching

Relevant Equations:

calculus
Someone told me to use parametric equations to find symmetries first
but are there other methods to sketch this graph?
How do you think
 

Answers and Replies

  • #2
138
61
Take x^2 axis and y axis. The figure is the circle centered at (5,0) with radius 4. Then it is easy to transform it to x-y axes.
 
Last edited:
  • #3
5
1
Yeah that's interesting
Take x^2 axis and y axis. The figure is the circle centered at (5,0) with radius 4. Then it is easy to transform it to x-y axes.
actually I don't know how to transform x^2 y axis to xy axis...
 
  • #4
138
61
x^2=1 corresponds x=-1,1
x^2=9 corresponds x=-3,3
x^2=5 corresponds x=-sqrt5, sqrt5, etc.
You then got six (x,y) points.

Edit: not six, eight (x,y) points
 
Last edited:
  • #5
5
1
x^2=1 corresponds x=-1,1
x^2=9 corresponds x=-3,3
x^2=5 corresponds x=-sqrt5, sqrt5, etc.
You then got six (x,y) points.
got it thanks
 
  • #6
epenguin
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  • #7
kuruman
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Now that you know that the circle is centered at (5,0) and has radius 4 units, to sketch it without a calculator or software, get a cheap compass, spread it to a distance of 4 units, put the pointy end at (5,0) units and draw the circle. You can also do it with a nail, some string and a pencil.
 
  • #8
epenguin
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You also easily get x co-ordinates of four points where y = 0, and symmetry tells you something about their special nature.
 

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