How to solve quadratic equation in x and y?

Hello everyone,

Could someone help me, please?

I would like to solve this quadratic equation:

f(x,y) = 3x^2 - 6y^2 + 1

and plot it in the 3D space. For the surface in the space I would like to have the x, y couples of data.

Thank you very much

Laura

Answer 1

[Star Strider]

I am not certain what solve is in this context.

Plotting the function is straightforward —

syms x y 
f(x,y) = 3*x^2 - 6*y^2 + 1

f(x, y) = 

figure
fsurf(f, [-5 5  -5 5])

.

[Star Strider]

My pleasure!

I am not certain how successful that will be, however one possibility would be —

syms x y 
f(x,y) = 3*x^2 - 6*y^2 + 1

f(x, y) = 

S = solve(f, [x,y])

S = struct with fields:
    x: [2×1 sym]
    y: [2×1 sym]

S.x

ans = 

S.y

ans = 

There is one equation in two unknowns, so no unique solution for both ‘x’ and ‘y’ exists. This is the best (and only) possible outcome, other than solving for one in therms of the other.

.

[laura bagnale]

Thank you very much, again!

About your comment, for solving y in terms of x, the procedure would be:

s = solve(f, [y])?

Thank you

[Star Strider]

My pleasure!

Yes.

syms x y 
f(x,y) = 3*x^2 - 6*y^2 + 1

f(x, y) = 

S(y) = solve(f, x)

S(y) = 

S(x) = solve(f, y)

S(x) = 

.

[laura bagnale]

Thank you very much

This was helpful!

[Star Strider]

As always, my pleasure!

.

Answer 2

[laura bagnale]

Thank you very much for your reply, Star Strider.

Sorry, I was unclear.

I meant f(x,y) = 3*x^2 - 6*y^2 + 1 == 0, so I need to find the couple (x,y), real, that very this equation.

Thank you a lot

Laura