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 [tex]z_1=x_1+iy_1\text{ and } z_2=x_2+iy_2[/tex] is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The radius of the circle is
[tex]d=\sqrt{(19-4)^2+(-13-(-5))^2}=17[/tex]
The radius of the circle is 17 units.
The distance between –11 –3i and (4-5i).
[tex]d=\sqrt{(-11-4)^2+(-4-(-5))^2}=\sqrt{226}[/tex]
The distance between –4.5+3.5i and (4-5i).
[tex]d=\sqrt{(-4.5-4)^2+(3.5-(-5))^2}=12.02[/tex]
The distance between -12+10i and (4-5i).
[tex]d=\sqrt{(12-4)^2+(10-(-5))^2}=17[/tex]
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).
[tex]d=\sqrt{(21-4)^2+(12-(-5))^2}=21.93[/tex]
Therefore option 3 is correct.
