Question

Find the diameter of the circle whose centre is at (2, 0) and which passes through the point (7, -12).

Answer 1

Let AB  be a diameter of the circle having its centre at C(2,0) such that the coordinates of A are (7,-12)


Let the coordinates of B be ( x,y)


Since C is the midpoint of AB . Therefore the coordinates of C are



[coordinates of mid point = ((x1+x2)/2, (y1+y2)/2]



((x+7)/2,( y-12)/2)


But the coordinates of C are (2,0) (given)


(x+7)/2 = 2          &.        (y-12)/2 = 0


x+7=4     & y-12=0


x= 4-7    & y=0+12


x= -3      &  y=12


Hence the coordinates of B are ( -3,12)


Here A(7,-12) B ( -3,12)


x1= 7 , x2 = -3, y1= -12, y2= 12


Diameter= distance between A and B


AB= √ (x2 - x1)² + (y2-y1)²


= √ (-3 -7)²+(12-(-12))²


= √ (-10)² + (24)²


= √ 100+ 576


= √ 676= √26× 26


AB= 26 UNITS


Hence, the diameter of the circle is 26 units

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Hope this will help you...

Answer 2

hope this will help you