quadratic curve from matrices determinant

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laura bagnale
laura bagnale 2021-6-14
回答： Ishu 2024-5-5
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
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Catalytic
Catalytic 2021-6-14
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
laura bagnale 2021-6-14
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

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回答（1 个）

Ishu
Ishu 2024-5-5
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!

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