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KCET2009MathematicsCircle

If the circle x ²+ y ²= a ² intersects the hyperbola xy = c ² in four points P (x₁, y₁ ), Q (x₂, y₂ ), R (x₃, y₃ ) and S (x₄, y₄ ) , then

Options

  1. Ay ₁+ y ₂+ y ₃+ y ₄=2
  2. Bx ₁ x ₂ x ₃ x ₄=2 c ⁴
  3. Cy ₁ y ₂ y ₃ y ₄=2 c ⁴
  4. Dx ₁+ x ₂+ x ₃+ x ₄=0

Correct answer

D. x ₁+ x ₂+ x ₃+ x ₄=0

Step-by-step solution

Given, x²+y²=a² and x y=c² aligned & & x²+ ( c² x )² &=a² & & x⁴-a² x²+c⁴ &=0 & & x₁+x₂+x₃+x₄ &=0 aligned

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