Monday

April 21, 2014

April 21, 2014

Posted by **mike** on Friday, May 8, 2009 at 12:43am.

ax^2+cy^2+dx+ey+f=0

if the equation represents an ellipse and then when it represents a hyperbola.please help.

- math -
**Count Iblis**, Friday, May 8, 2009 at 8:43amPut

x_1 = x

x_2 = y

Then the quadratic form is of the form

Sum over i and j of

M_{i,j}x_i x_j = constant.

Then, since this equation is invariant under orhtogonal transformations, we can write it in diagonal form. If you define new coordinates x' and y' that are in the direction of the two egienvectors, the equation becomes:

lambda_1 x'^2 + lambda_2 y'2 = constant

where lambda_1 and lambda_2 are the two eigenvalues of M.

- math -
**Count Iblis**, Friday, May 8, 2009 at 8:46amI now see that there is no xy term in your expression, so the problem is trivial. You can simply complete the square, no need to diagonalize a matrix.

**Related Questions**

math - how would you determine the eccentricity of the conic section when ...

algebra 2 - 1) In the general second-degree equation Ax^2 + Bxy + Cy^2 + Dx + Ey...

algebra 2 - Determine values for A, B, and C such that the equation below ...

algebra 2 - Determine values for A, B, and C such that the equation below ...

Algebra II - I am lost on this one!!! Determine values for A, B, and C such that...

algebra help please - I notice that other problems are answered in a timely ...

MATH!+ check please~ thanks in advance! - the equation 2x^2+ cy^2+Dx+Ey+f= 0 ...

pre cal - What is the center of the conic whose equation is x^2 + 2y^2 - 6x + ...

pre-calculus - How do i know if a conic section is a circle, ellipse, hyperbola...

math - Classify the conic section as a circle, an ellipse, a hyperbola, or a ...