The eccentricity of the ellipse 9 x^2+5 y^2-30 y=0 is

Step-by-step solution

To determine the eccentricity of the ellipse defined by 9x^2 + 5y^2 - 30y = 0 , the equation is first transformed into standard form by completing the square. Rewriting the equation: 9x^2 + 5(y^2 - 6y) = 0 . Completing the square: 9x^2 + 5[(y - 3)^2 - 9] = 0 , which simplifies to 9x^2 + 5(y - 3)^2 = 45 . Dividing through by 45 yields the standard form: x^2 5 + (y - 3)^2 9 = 1 . The larger denominator, a^2 = 9 , corresponds to the semi-major axis, while b^2 = 5 is the semi-minor axis squared. The eccentricity is giv