A circle has center at –6 + 2i and a point on the circle at 4 + 26i. Which of the following points is also on the circle? –19 + 15i –16 – 22i 6 + 16i 20 – 24i

The correct option is (B) -16-22i

Explanation:
First let us use the equation of a circle:
[tex](x-x_o) + (y-y_o) = r^2[/tex]

Since [tex](x_o,y_o) = (-6,+2)[/tex]

So the equation becomes:
[tex](x+6) + (y-2) = r^2[/tex] --- (1)

Now find r^2 using the given point (4,26):
[tex](4+6) + (26-2) = r^2 \\ 10+24 = r^2 \\ r^2 = 34 [/tex]

Now from the given options, the one that would give us r^2 = 34 or r^2 = -34 is:
(-16-22i)

Put (-16,-22) in (1):
(1) => r^2 = (-16+6) + (-22-2) = -34

Hence the correct option is (B) -16-22i