If s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)what does y equal?
A. \(\sqrt{\frac{(b^2 - a^2)}{(s^2 - x^2)}}\)
B. \(\sqrt{\frac{(b^2 - a^2)}{(s^2 \times 2)}}\)
C. \(\sqrt{\frac{x^2 - a^2 - b^2}{s}}\)
D. \(\frac{x^2 - a^2 - b^2}{s}\)
E. \(\sqrt{\frac{(b^2 x^2)}{(a^2 - s^2 x^2)}}\)
Correct Answer: E
Explanation
s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)
s\(^2\) = \(\frac{a^2}{x^2} - \frac{b^2}{y^2}\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2}{x^2}\) - s\(^2\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2 - s^2 x^2}{x^2}\)
\(\frac{1}{y^2}\) = \((\frac{a^2 - s^2 x^2}{x^2}) \times \frac{1}{b^2}\)
\(\frac{1}{y^2}\) = \(\frac{a^2 - s^2 x^2}{b^2 x^2}\)
\(\therefore\) y\(^2\) = \(\frac{b^2 x^2}{a^2 - s^2 x^2}\)
y = \(\sqrt{\frac{b^2 x^2}{a^2 - s^2 x^2}}\)
