Finding the Centre of a Circle Passing Through Given Points (1,-2) and (4,-3)

[zorro]

Homework Statement

Find the centre of the circle which passes through the points (1,-2) and (4,-3) whose centre lies on the line 3x + 4y = 7

Homework Equations

The Attempt at a Solution

distance from the centre of the circle to the given points is equal
by distance formula and simplifying,
I got 3x-2y=10

On Solving 3x + 4y= 7 and 3x - 2y= 10
I got the point (3,-1/2) as the centre of the circle.
But answer is something else.
Please help

 

[betel]

I get as a second equation
$$3x -y=10$$

 

[zorro]

Damn! such a silly mistake
Thanks mate.