Question:
An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is <span class="math-inline">\frac{2}{3}</span> then the eccentricity of the ellipse is:
\frac{2\sqrt{2}}{3}
\frac{\sqrt{5}}{3}
\frac{8}{9}
\frac{2}{3}
Step-by-Step Solution
Key Concept: General
(2h - 3α)^2 + (2k - 3β)^2 = 9a^2
Correct Answer: 9a^2