Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line

Q. Consider a family of circles which are passing through the point (–1, 1) and has x-axis as its tangents. If (h, k) are the co-ordinates 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 $\le$ $\frac{1}{2}$

Q. If a circle S(x, y)=0 touches the line x + y = 5 at the point (2, 3) and S(1, 2) = 0, then the radius of such circle is .

1. $r=\frac{3}{2}\mathrm{units}$
2. $r=\frac{1}{2}\mathrm{units}$
3. $r=\frac{3}{\sqrt{2}}\mathrm{units}$
4. $r=\frac{1}{\sqrt{2}}\mathrm{units}$

Q.

Find the equation of the circle passing the point (1, 2) and touching the line 2x + y - 1 = 0 at the point (1, -1).

1. $x^2+y^2+8x+y+y=0$

2. $x^2+y^2-4x-2y+5=0$

3. $x^2+y^2-8x-y+5=0$

4. $x^2+y^{2}4x+2y-5=0$