Answer:
The correct option is 3.
Step-by-step explanation:
The center of the circle is (4-5i). A point on the circle at (19 – 13i).
Distance formula between two points \(z_1=x_1+iy_1\text{ and } z_2=x_2+iy_2\) is
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The radius of the circle is
\(d=\sqrt{(19-4)^2+(-13-(-5))^2}=17\)
The radius of the circle is 17 units.
The distance between –11 –3i and (4-5i).
\(d=\sqrt{(-11-4)^2+(-4-(-5))^2}=\sqrt{226}\)
The distance between –4.5+3.5i and (4-5i).
\(d=\sqrt{(-4.5-4)^2+(3.5-(-5))^2}=12.02\)
The distance between -12+10i and (4-5i).
\(d=\sqrt{(12-4)^2+(10-(-5))^2}=17\)
The distance between -12+10i and (4-5i) is equal to the radius. Therefore point 12+10i lies on the circle.
The distance between 21+12i and (4-5i).
\(d=\sqrt{(21-4)^2+(12-(-5))^2}=21.93\)
Therefore option 3 is correct.
