# Thread: 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!!!

2. Hello and welcome to MathHelpForum.
You should understand that this is not a homework service nor is it a tutorial service. Please either post some of your own work on these problems or explain what you do not understand about the question. Moreover, we discourage posting a whole list of problems at one time, especially if you show no effort.

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 $\displaystyle (p,5)$.