equation of the circle passing through A(1,2),B(5,2)such that the angle subtended by AB at points on the circle is pi/4​

P is the midpoint P=(3,2)

Step-by-step explanation:in ΔAOB

AB  

2

=2r  

2

(5−1)  

2

+(2−2)  

2

​  

=4

2r  

2

=16

r=2  

2

​  

slopeOM×slopeOB=−1

α−3

p−2

​  

×  

5−1

2−2

​  

=−1

α−3

p−2

​  

×0=−1

AB∥x−axis

OM∥y−axis

⇒α=3

OA=r=2  

2

​  

(3,1)(1,2)=2  

2

​  

(3−1)  

2

+(p−2)  

2

=8

p=0,4

Center(3,0)

r=2  

2

​  

(x−3)  

2

+y  

2

=8

Center(3,4)

r=2  

2

​  

(x−3)  

2

+(y−4)  

2

=8

​