Question

the centre of a circle is (2x-1,3x+1). find the x if the circle is passes thuthe centre of a circle is (2x-1,3x+1). find the x if the circle is passes through (-3, -1) and the length of its diameter is 20 units.gh (ro-3, -1) and the length of its diameter is 20 units.

Answer 1

There sure is a lot of gobbledegook there.

If we say that the center lies on the line
x = 2t-1
y = 3t+1

Apparently the center of the circle lies on the line y = (3x+5)/2

The circle passes through (-3,-1)

So, we need

(-3-h)^2 + (-1-(3h+5)/2)^2 = 100
h=3 or -105/13
so, k= 7 or -125/13

h=3 means x = 2
h = -105/13 means x = -223/13

So, there are two circles that meet the need,with centers at
(3,7) or (-105/13,-125/13)

The graph below shows that the circle intersects the line at (-3,-1)

http://www.wolframalpha.com/input/?i=plot+(x-3)%5E2+%2B+(y-7)%5E2+%3D+100,+y%3D(3x%2B5)%2F2