# Math Help - Solve the equations of these circles

1. ## Solve the equations of these circles

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!!!

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3. Thank you for the advice.
I have these questions solved but I do not know whether they are correct. Except for the last one.
Question 1
(i) 4
(ii)Centre
(iii)(x-6)^2+(y-4)^2+16
Question 2
(i)4
(ii)(4,5)
(iii) (x-4)^2+(y-5)^2=16
Question 3
And the center looks like $(p,5)$.