Question

if AB is a diameter of circle C(O,r) where coordinates of A and B are (5,6) and (3,-2) respectively find coordinates of O

Answer 1

Answer:

Let the coordinates of the one end of a diameter AB of a circle are A(2,3) and B(x,y).

Let the coordinates of the center of the circle C(−2,5).

As center is the midpoint of the diameter AB so the coordinates of center is

C(

2

2+x

,

2

3+y

)

Now equating the coordinates of center we get

2

2+x

=−2

⇒2+x=−4

⇒x=−4−2

⇒x=−6

2

3+y

=5

⇒3+y=10

⇒y=10−3

⇒y=7

∴Coordinates of B=(−6,7).