Q96 / 160 · TS EAMCET 2009 · Mathematics

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

  • Correct answer
    A
    0
  • B
    $c$
  • C
    $a$
  • D
    $c^4$

Solution

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. $\therefore \quad y_1+y_2+y_3+y_4=0$

Hence, the correct answer is option: 'A'.

More Hyperbola Questions