Question
Question: If the equation \|z – z<sub>1</sub>\|<sup>2</sup> + \|z – z<sub>2</sub>\|<sup>2</sup> = k represents...
If the equation |z – z1|2 + |z – z2|2 = k represents the equation of a circle, where z1 = 2 + 3i, z2 = 4 + 3i are the extremities of a diameter, then the value of k is
A
1/ 4
B
4
C
2
D
None of these
Answer
4
Explanation
Solution
Sol. As z1 and z2 are the extremities of the diameter,
|z – z1|2 + |z – z2|2 = |z1 – z2|2
⇒ k = |z1 – z2|2 = |2 + 3i – 4 – 3i|2 = |– 2|2 = 4