The Attempt at a SolutionReduce Ellipse: Centre & Eccentricity

[zorro]

Homework Statement

Reduce the given ellipse in standard form and find its centre and eccentricity.

4(x-2y+1)² + 9(2x+y+2)² = 25

Homework Equations

Rotation of axes
x=Xcosθ - Ysinθ
y=Xsinθ + Ycosθ

 

[HallsofIvy]

I would not use the "rotation of axes" formulas. Instead, let X= x- 2y and Y= 2x+ y so that your equation becomes
$$\frac{4}{25}(X- (-1))^2+ \frac{9}{25}(Y- (-2))^2= 1$$

What is the center and eccentricity of that ellipse? Now go back to x and y coordinates.

 

[zorro]

Wow! that is a very nice method. Thanks!