Equation of Circle

1.Center on line x=3, tangent y-axis at (0, 5)

The circle  will have its center at  (3, 5)  and since it is tangent to the y axis, the radius will be 3.....so....the equation is

(x - 3)^2  + (y - 5)^2  = 9

Here's the graph : https://www.desmos.com/calculator/sejlwks7kv

2.Radius 4, tangent to x-axis; contain (–5,8)

The center must be (-5, 4).....so the equation is

(x + 5)^2  +  ( y - 4)^2  =  16

Graph here : https://www.desmos.com/calculator/4r1rrwt5pq

3. Radius 5, tangent to y-axis; contain (10,7)

The center is (5,7)   and the radius is 5......the equation  is

(x - 5)^2  + ( y - 7)^2  = 25

https://www.desmos.com/calculator/70z6uvpvh7

4.Center on line y–4=0, tangent x-axis at (–2, 0)

Note......adddig 4 to both sides of the equation produces  y  = 4

So....since it is tangent to the x axis...the radius is 4

And the center is (-2, 4)

So the equation is

(x + 2)^2  +  ( y - 4)^2  =  16

https://www.desmos.com/calculator/edaxudoeg7