quadratic curve from matrices determinant

Hello everyone,

could someone help me please?

I would like to obtain the quadratic curve coming from the calculation of a 2x2 matrix determinant.

This is what I wrote in my code:

h = @(x,y,z) 3.*(x+5).^2 + (x + 5).*(y - 2) + (y - 2).^2;

syms x y z

w = h(x,y,z)

g = @(x,y,z) (x - 5).^2 - (x - 5).*(y - 3) + (y - 3).^2;

syms x y z
w1 = g(x,y,z)

Dhx = diff(h,x)
Dhy = diff(h,y)

Dgx = diff(h,x)
Dgy = diff(h,y)

p1 = Dhx * Dgy
expand(p1)
p2 = Dhx * Dgy
expand(p2)

exp1 = expand(p1)
exp2 = expand(p2)

Now I should do the difference between exp1 and exp2, but I can't do it.

I am new with the symbolic toolbox, so I have difficulties to pass from symbolic expressions to numerical values.

I guess there is a faster way to calculate the determinant of my matrix and thus get the quadratic function but I don't really know how to find it.

Thank you very much for your support!

Laura

[laura bagnale]

Sorry there was an error in Dgx, Dgy:

Dgx = diff(g,x)
Dgy = diff(g,y)

A = [Dhx Dhy; Dgx Dgy]

det(A)

this is the complete code that I wrote.

Is it correct?

Thanks a lot!

[Catalytic]

You have a number of previous posts that you have not accepted answers to, though the answers seem to be fine. It is a disincentive for people to help you.

[laura bagnale]

Oh OK, thank you very much.

I'm very sorry but I'm new and I didn't understand that it was important!

Thank you again!

Laura

Answer 1

[Ishu]

Hi Laura

I understand that you want to determine the type of quadratic curve from a given quadratic curve with the help of matrix determinat.

If you have a quadratic curve of the form "Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0" then the matrix representation of the quadratic part is [A, B/2; B/2, C]. From this matrix you can calculate the deteminant of the equation. If the determinat is less than 0 then the curve is a "hyperbola" and if determinat is greater than zero then the curve is "ellipse".

%Example on how to calculate determinant.
% Define the coefficients of the quadratic equation
A = -8; B = 8; C = 4; D = -29; E = 70; F = -21;

% Construct the matrix Q
Q = [A, B/2; B/2, C];

% Calculate the determinant of Q
detQ = det(Q);

Hope it helps!