The x-axis and the line y=8 are both tangents to a circle k.

The centre of the circle lies on the line 2x-3y=0

(i) Write down the length of the radius.

(ii)Find the coordinates of the centre of the circle.

(iii)Write down the equation of the circle.

That is question 1

Question 2:

The y-axis and the line x=8 are tangents to a cricle.

The centre of the circle lies on the line 2x-y-3=0.

(i)Write down the length of the radius of the circle.

(ii)Find the coordinates of the centre of the circle.

(iii)Find the equation of the circle.

Question 3

A circle touches the y-axis at the point (0,-3) and it contains the point (4,1).

Find the equation of this circle

Question 4

The x-axis and the line y=10 are tangents to a circle.

If the circle also contains the point (1,5), find the equations of the two circles that satisfy these conditions.

Thanks any help is much appreciated!!!