Equation of circle with (h,k) as center

Q.

The distance between the vertex of the parabola $y=x^2-4x+3$and the centre of the circle $x^2=9-{\left(y-3\right)}^2$ is

1. $2\sqrt{3}$ units

2. $3\sqrt{2}$ units

3. $2\sqrt{2}$ units

4. $\sqrt{2}$ units

5. $2\sqrt{5}$ units

Q. Equation of a circle whose centre is origin and radius is equal to the distance between the lines x = 1 and x = -1 is

1. $x^2+y^2=4$
2. $x^2+y^2=1$
3. $x^2+y^2=-4$
4. $x^2+y^2=\sqrt{2}$

Q. The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y - 4x + 3 = 0, is

1. $x^2+y^2+4x-10y+25=0$
2. $x^2+y^2-4x-10y+16=0$
3. $x^2+y^2-4x-10y+25=0$
4. $x^2+y^2-14y+8=0$

Q. The equation of circle passing through (4, 5) and having the centre at (2, 2), is

1. $x^2+y^2+4x+4y-5=0$
2. $x^2+y^2-4x-4y-5=0$
3. $x^2+y^2-4x=13$
4. $x^2+y^2-4x-4y+5=0$