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

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

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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:
• OmCheeto and GravitySK
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...

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:
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

• HallsofIvy
epenguin
Homework Helper
Gold Member
got it thanks
Can we see?

• OmCheeto
kuruman