If the points lie on a circle, then what is/are the possible value(s) of k ?

For the next two (02) items that follow : Consider the points A(0, 2), B(2, 3), C(4, 5) and D(0, k).

  1. A. 2 only
  2. B. 5 only
  3. C. 2, 17
  4. D. 5, 17

Correct Answer: C. 2, 17

Explanation

Substituting the coordinates of A, B, and C into the general circle equation yields \( x^2 + y^2 + 5x - 19y + 34 = 0 \). Substituting D(0, k) into this gives \( k^2 - 19k + 34 = 0 \), whose roots are 2 and 17.

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