The correct option is B x2+y2+6x+2y−15=0
Let the centre of the circle be (h,k)
Given tangent is 4x+3y=10
It passes through (1,2)
Line passing through (1,2) and centre is perpendicular to the given tangent, so
k−2h−1=34⋯(1)
Now, the radius of circle
√(h−1)2+(k−2)2=5⇒(h−1)2+(k−2)2=25
Using equation (1), we get
⇒(h−1)2+916(h−1)2=25⇒(h−1)2=16⇒h−1=±4⇒h=5,−3⇒k=5,−1
Hence, the circles are
x2+y2−10x−10y+25=0 and
x2+y2+6x+2y−15=0