In the diagram below, a circle with centre O is given with diameter AB. The coordinates of A and B are (4 ; 4) and (2 ; -6) respectively. ya A(4; 4) B(2; -6) a) Determine the coordinates of O, the centre of the circle. b) Calculate the length of the radius of the circle. c) Write down the equation of the circle in form: (x−a)2+(y−b)2=r2 d) Write down the equation of the circle in form: ax2+bx+cy2+dy+e=0

Question

In the diagram below, a circle with centre O is given with diameter AB. The coordinates of A and B are (4 ; 4) and (2 ; -6) respectively. ya A(4;  4) B(2; -6)  a) Determine the coordinates of O, the centre of the circle.  b) Calculate the length of the radius of the circle.  c) Write down the equation of the circle in form:  (x−a)2+(y−b)2=r2  d) Write down the equation of the circle in form:  ax2+bx+cy2+dy+e=0

macalpinee3 · Accepted Answer

Step 1  Centre of the circle = mid Point of AB  =(x1+x22, y1+y22)  (4+22, 4−62)  =(3, −1)  Step 2  Length of the radius =AB2  =(x2−x1)2+(y2−y1)22  =(4−2)2+(4+6)22  =4+1002  r=1042

Orlando Paz · Accepted Answer

Step 1    Equation of the circle in form of    (x−a)2+(y−b)2=r2    (x−3)2+(y+1)2=(1042)2    (x−3)2+(y+1)2=1044    (x−3)2+(y+1)2=26    Step 4    Equation of the circle in form of    ax2+bx+cy2+dy+e=0    (x−3)2+(y+1)2=26    x2+9−6x+y2+1+2y−26=0    x2−6x+y2+2y−16=0

In the diagram below, a circle with centre O is given with d

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