Finding the eccentricity of an ellipse.?

Question

49x^2 - 588x + 9y^2 - 144y + 1899 = 0

That is the problem, please help me!!!

Answer 1

First, use the "complete the square" technique to put the equation in standard form. You should get

[(x-6)²]/9 + [(y-8)²]/49 = 1

From this we read off that

a = 7 (semi-major axis)
b = 3 (semi-minor axis)

Then the eccentricity e is given by

e = √[1 - (b²/a²)]

so the eccentricity is √(1 - 9/49) = √(40/49) = (2√10)/7