Question

Find the eccentricity of the ellipse.

x^2 + 9y^2 - 10x + 36y + 52 = 0

Answer 1

Step 1:

The equation of ellipse is .

Re-write the equation.

Divide each side by 9.

The standard form of ellipse equation is ,

where is center, is the length of semi-major axis and is length of semi-minor axis.

Compare the equation with standard form of ellipse.

Center .

Semi-major axis length is .

Semi-Minor axis length is .

Step 2:

Find eccentricity.

For ellipse: .

Eccentricity .

.

Solution:

Eccentricity of the ellipse is .