The foci of the ellipse 4x^{2}+9y^{2}=1 are at Q and R. If P(x,y) is any point on the ellipse, then what is PQ+PR equal to?

Explanation

Rewriting the ellipse equation in standard form gives \frac{x^2}{1/4} + \frac{y^2}{1/9} = 1. Here a^2 = 1/4 implies a = 1/2. By the fundamental property of an ellipse, the sum of distances from any point on the curve to the two foci is equal to the length of the major axis 2a. Thus, PQ + PR = 2(1/2) = 1.

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