Answer:
Option 4 : 16+24i
Step-by-step explanation:
Given a circle has a diameter with end points at(15+25i) and (-25-17i)
Centre would be the mid point of these two points
Centre = [tex](\frac{15-25}{2} ,\frac{25-17}{2} )\\= -5+4i[/tex]
Out of given four points to find which point lies on the circle
If a point lies on the circle then it would have distance from centre equal to radius.
Radius = distance between two given points/2
=[tex]\frac{1}{2} \sqrt{(15+25)^2+(25+17)^2} \\=\frac{58}{2} \\=29[/tex]
Let us calculate distance form each point.
i)-15+2i: distance from -5+4i= 10.19
ii) 0+0i : distance from -5+4i = 6.40
iii) 15+17i : Distance from -5+4i = 23.85
iv) 16+24i: distance from -5+4i= 29
Hence only 4th point lies on the circle
