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: Option 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}})