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If the circle $x^2+y^2=a^2$ intersects the hyperbola $x y=c^2$ in four points $\left(x_i, y_i\right)$, for $i=1,2,3$ and 4 , then $y_1+y_2+y_3+y_4$ equals
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Given,
$\begin{array}{rlrl}
\text { Given, } & & x^2 y^2 & =c^4 \\
\Rightarrow & y^2\left(a^2-y^2\right) & =c^4 \\
\Rightarrow & y^4-a^2 y^2+c^4 & =0
\end{array}$
Let $y_1, y_2, y_3$ and $y_4$ are the roots.
$\therefore \quad y_1+y_2+y_3+y_4=0$
$\begin{array}{rlrl}
\text { Given, } & & x^2 y^2 & =c^4 \\
\Rightarrow & y^2\left(a^2-y^2\right) & =c^4 \\
\Rightarrow & y^4-a^2 y^2+c^4 & =0
\end{array}$
Let $y_1, y_2, y_3$ and $y_4$ are the roots.
$\therefore \quad y_1+y_2+y_3+y_4=0$
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