Question

A circle has a diameter with endpoints at 15 + 25i and –25 – 17i. Which point is also on the circle? –15 +21i 0 + 0i 15 + 17i 16 + 24i

Answer 1

Option 4 : 16+24i

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 =
`((15-25)/(2) ,(25-17)/(2) )\\= -5+4i`

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

=
`(1)/(2) √((15+25)^2+(25+17)^2) \\=(58)/(2) \\=29`

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