Question 398173
The centre of a circle is (2x-1,7) and it passes through the point (-3,-1).If the diameter of the circle is 20units ,then find the values of x.

let us first start with the standard form for a circle.

(x-h)^2+(y-k)^2=r^2
(h,k)= coordinates of the center
r=radius of the circle

given: 
diameter=20 or radius=10
y-coordinate of the center
point on circle (-3,-1)
let u=(2x-1),the x-coordinate of the center

solving:
(x-u)^2+(y-7)^2=10^2
(x-u)^2+(y-7)^2=100
x^2-2ux+u^2+y^2-14y+49=100
substitute (x,y) coordinates, (-3,-1)
9+6u+u^2+1+14+49=100
u^2+6u=100-73=27
u^2+6u-27=0
(u+9)(u-3)=0
u=-9
u=3

2x-1=u=-9
2x=-8
x=-4

2x-1=u=3
2x=4
x=2

ans:
x=-4
x=2

These are two circles with different centers,(-9,7) and (3,7)