Family of Circles

Q. The equations to the circles which touch the lines 3x – 4y + 1 = 0, 4x + 3y – 7 = 0 and pass through (2, 3) are

1. + - 4x - 16y + 43 = 0, 5 + 5 - 12x - 24y + 31 = 0
2. + + 4x + 16y - 43 = 0, 5 + 5 - 12x - 24y + 31 = 0
3. + - 4x - 16y + 43 = 0, 5 + 5 + 12x + 24y + 31 = 0
4. + + 4x + 16y - 43 = 0, 5 + 5 + 12x + 24y + 31 = 0

Q. Consider a family of circles which are passing through the point (-1, 1) and are tangent to the x-axis. If (h, k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval

1. $0<k<\frac{1}{2}$
2. $k\ge \frac{1}{2}$
3. $-\frac{1}{2}\le k\le \frac{1}{2}$
4. $k\le \frac{1}{2}$