Too complex?

Algebra Level 4

Let Z denote any complex number of the type \( x + iy \) in the complex plane. Then \[ \displaystyle |Z - \left( 3 + 4i \right) | + |Z - \left( 15 + 9i \right) | = K \] where K is any real number, represents

\( \) A. Ellipse when \( K = 13 \)

\(\) B. Ellipse when \( K > 13 \)

\( \) C. A line segment when \( K = 13 \)

\( \) D. A circle.

How many of the above statements are correct?

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