Help with circle geometry!
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
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'