Question

A circle passes through the points 0(0, 0), A(8, 4) and B(6, 6).
find the equation of this circle.

Answer 1

Answer:

25

Step-by-step explanation:

Let the equation of the general form of the required circle be  

x  

2

+y  

2

+2gx+2fy+c=0....(1)

According to the problem, the above equation of the circle passes through the points (0,6),(0,0) and (8,0). Therefore,

36+12f+c=0  ………. (2)

c=0                       ……………. (3)

64+16g+c=0  ……………. (4)

Putting c=0 in (2), we obtain f=−3. Similarly put c=0 in (4), we obtain g=−4

Substituting the values of g,f and c in (1), we obtain the equation of the required circle as:

x  

2

+y  

2

+2(−4)x+2(−2)y+0=0 that is  

x  

2

+y  

2

−8x−4y+0=0 can be rewritten as

x  

2

+y  

2

−8x−4y+16+9=0+16+9

(x−4)  

2

+(y−3)  

2

=25

Therefore, the equation of circle is (x−4)  

2

+(y−3)  

2

=25.

Answer 2

Answer:

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