I have a series of questions that I did. They lead up to the last question I can't solve. Could you check my math and help me with the last question? Thanks!

a) Let a be the point (2,3). Compute the distance from Origin 0 to A

answer: a^2 + b^2 = c^2
3^2 + 2^2 = c^2
c=sqrt(13)

b) find the equation of circle C passing through point A

x^2 + y^2 = 13 -> since the center is (0,0), right?

c) find the equation of line D tangent to the circle C at point A
since the equation for line OA is y=3/2 x + 0 , I can use the negative inverse of the slope to get the slope of the tangent, right?
so I used y=-2/3 x +b and input the coordinates (2,3) to get b

3 = (-2/3)(2) + b

b = 4 , therefore the equation of the tangent is y=-2/3 x + 4 right?

d) line D meet Ox at point B. Find the coordinates of B.
This is where I'm a little confused. Does "Ox" mean the x-axis? That's what I went on so I just used the previous line equation and set y to zero:

0= -2/3 x + b
x = 6 therefore line D meets Ox when x=6 coordinates (6,0)

e) compute distance of AB
A(2,3) B(6,0) I used Pythagoreans theorem and got a distance of 5

f) find the equation of the circle C' with center B and passing through A

since the circle equation is (x-h)^2 + (y-k)^2 = R^2 I just input everything I knew so far and got: (x-6)^2 + y^2 = 25

is all that correct? I know it's a lot but I appreciate the help!

The last question is:

g) find the coordinates of the intersection points of C and C'

To find the intersection points of two circles, C and C', their equations should be set equal to each other and solved.

The equation of circle C is given as x^2 + y^2 = 13, and the equation of circle C' is (x-6)^2 + y^2 = 25.

Setting these two equations equal to each other, we get:

x^2 + y^2 = (x-6)^2 + y^2

Expanding the equation:

x^2 + y^2 = x^2 - 12x + 36 + y^2

Simplifying:

12x = 36

Dividing both sides by 12:

x = 3

Now, plugging the value of x back into one of the original equations, let's use the equation of circle C:

3^2 + y^2 = 13

9 + y^2 = 13

y^2 = 4

Taking the square root of both sides:

y = ±2

Therefore, the two intersection points are (3, 2) and (3, -2).

So, the coordinates of the intersection points of circles C and C' are (3, 2) and (3, -2).