Question

A circle with center (3,5) intersects the y-axis are(0,1). find the radius of the circle, find the coordinates of the other point of intersection with the y-axis. what are the coordinates of the point of intersection of the circle and the x-axis

Answer 1

I would use the distance formula to solve this problem:

Distance formula: $\sqrt{( x_{2} - x_{1} )^2 + ( y_{2}- y_{1})^2 }$

(x1,y1) = (3,5)
(x2,y2)= (0,1)


Plug in points to find radius:
r=$\sqrt{( x_{2} - x_{1} )^2 + ( y_{2}- y_{1})^2 }$
r=$\sqrt{( 0 - x_{1} )^2 + ( 1- y_{1})^2 }$
r=$\sqrt{( 0 - 3 )^2 + ( 1- 5)^2 }$
r=$\sqrt{( - 3 )^2 + ( - 4)^2 }$
r=$\sqrt{(9 + 16 )}$
r=$\sqrt{(25)}$
r= 5 units


To find the other point on the circle that crosses the y-axis change the sign of y2.

(x1,y1) = (3,5)
(x2,y2) = (0,-1)