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

[GravitySK]

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

 

[mitochan]

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.

 

[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...

 

[mitochan]

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

 

[GravitySK]

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

 

[epenguin]

got it thanks

Can we see?

 

[kuruman]

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.

 

[epenguin]

You also easily get x co-ordinates of four points where y = 0, and symmetry tells you something about their special nature.