Question

Slope field identification?

Answer 1

Possible solutions:
y=Cx2
x=Cy2
y2 – x2 = C2
x2 + y2 = C2

Answer 2

I would pick a number to replace C with. For instance, C = 2

Then I would graph each answer choice

y = Cx^2 ---> y = 2x^2
x = Cy^2 ---> x = 2y^2
y^2-x^2=C^2 --> y^2 - x^2 = 4
x^2+y^2=C^2 --> x^2+y^2 = 4

then compare the basic shape of each curve to see if it fits the slopefield

Answer 3

or you can use a tool like desmos to interactively change C and that will show how the graphs change

https://www.desmos.com/calculator/dp6flhaiyb

Answer 4

Thanks so much!

Answer 5

No problem