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KCET2007MathematicsHyperbola

If x² 36 - y² k² =1 is a hyperbola, then which of the following statements can be true?

Options

  1. A(-3,1) lies on the hyperbola
  2. B(3,1) lies on the hyperbola
  3. C(10,4) lies on the hyperbola
  4. D(5,2) lies on the hyperbola

Correct answer

C. (10,4) lies on the hyperbola

Step-by-step solution

Given, x² 36 - y² k² =1 array ll & y² k² = x² 36 -1 & k²= 36 y² x²-36 array k²>0 If x²-36>0 x²>36 This is true only for point (10,4) . So, (10,4) lies on the hyperbola.

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