What is the sum of the intercepts of the line \frac{x}{a^{2}}+\frac{y}{b^{2}}=\frac{2}{a^{2}+b^{2}} on the coordinate axes?

  1. A. 2 ✓
  2. B. 1
  3. C. \frac{1}{2}
  4. D. a^{2}+b^{2}

Correct Answer: A. 2

Explanation

Rewrite the given equation in the standard intercept form \frac{x}{X_{int}} + \frac{y}{Y_{int}} = 1. It becomes \frac{x}{a^2[2/(a^2+b^2)]} + \frac{y}{b^2[2/(a^2+b^2)]} = 1. The sum of the intercepts is X_{int} + Y_{int} = \frac{2a^2}{a^2+b^2} + \frac{2b^2}{a^2+b^2} = \frac{2(a^2+b^2)}{a^2+b^2} = 2.

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