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COMEDK2020MathematicsHyperbola

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(5,2) lies on the hyperbola.
  4. D(10,4) lies on the hyperbola.

Correct answer

D. (10,4) lies on the hyperbola.

Step-by-step solution

We have, x² 36 - y⁸ k² =1 Option (a) (3,1) aligned 9 36 - 1 k² &=1 & 1 k² = -27 36 k²= -36 27 aligned which is not possible. Option (b) (-3,1) 9 36 - 1 k² =1 k²= -36 27 which is not possible. Option (c) (5,2) aligned 25 36 - 4 k² &=1 4 k² &= -11 36 k² &= -144 11 aligned which is not possible. Option (d) (10,4) 100 36 - 16 k² =1 16 k² = 64 36 k²=9 , which is possible.

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