If the circle $x^{2} + y^{2} = a^{2}$ intersects the hyperbola $xy = c^{2}$ 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

Question

Dr. Abubacker · Accepted Answer

(a)
Given, $x^{2}y^{2} = c^{4}$
$\Rightarrow \ y^{2}\left( a^{2} - y^{2} ight) = c^{4}$
$\Rightarrow \ y^{4} - a^{2}y^{2} + c^{4} = 0$
Let $y_{1},y_{2},y_{3}$ and $y_{4}\$ are the roots
$	herefore\ y_{1} + y_{2} + y_{3} + y_{4} = 0$

Q. If the circle $x^{2} + y^{2} = a^{2}$ intersects the hyperbola $xy = c^{2}$ 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

Explanation

Reviewed by Dr. Abubacker

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