TS EAMCET · Maths · Hyperbola
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
- A 0
- B \(c\)
- C \(a\)
- D \(c^4\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
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. \(\therefore \quad y_1+y_2+y_3+y_4=0\)
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