If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 in four points (x_i, y_i ) , for i=1,2,3 and 4 , then y₁+y₂+y₃+y₄ equals

Step-by-step solution

Given, array rlrl Given, & & x^2 y^2 & =c^4 & y^2 (a^2-y^2 ) & =c^4 & y^4-a^2 y^2+c^4 & =0 array Let y₁, y₂, y₃ and y₄ are the roots. y₁+y₂+y₃+y₄=0