Question

If the coordinates of the end points of a circle are A(1,2) B(5,6) then find the coordinate of the center of the circle​

Answer 1

Let AB be a diameter of the circle having its centre at C(1, -3) such that the coordinates of one end A are (4, -1).

Let the coordinates of B be (x,y).

Since C is the mid-point of AB. Therefore,the coordinates of C are(

2

x+4

,

2

y−1

).

But, the coordinates of C are given to be (1,-3).

∴

2

x+4

=1and

2

y−1

=−3

⇒x+4=2andy−1=−6

⇒x=−2andy=−5

Hence,the coordinates of B are (-2, -5).

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