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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

Respuesta :

wuzzleluver
I would use the distance formula to solve this problem:

Distance formula: [tex] \sqrt{( x_{2} - x_{1} )^2 + ( y_{2}- y_{1})^2 } [/tex]

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


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

The coordinates of the other point of intersection with the y-axis will be (0, 9). And the x-intercept is at (3, 0).

What is the equation of circle?

Let r be the radius of the circle and the location of the center of the circle be (h, k).

Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

A circle with center (3,5).

Then the equation of the circle will be

(x - 3)² + (y - 5)² = r²

The circle intersects the y-axis at (0,1).

Then the radius of the circle will be

(0- 3)² + (1 - 5)² = r²

             9 + 16 = r²

                    r² = 25

                      r = 5

Then the equation of the circle will be

(x - 3)² + (y - 5)² = 5²

Then the other y-intercept of the circle (0, a) will be

(0 - 3)² + (a - 5)² = 5²

        9 + (a - 5)² = 25

              (a - 5)² = 16

                 a - 5 = 4

                       a = 9

The intersection of the circle with x-axis at (b, 0) will be

(b - 3)² + (0 - 5)² = 5²

     25 + (b - 3)² = 25

              (b - 3)² = 0

                 b - 3 = 0

                       b = 3

Thus, the coordinates of the other point of intersection with the y-axis will be (0, 9). And the x-intercept is at (3, 0).

The graph is given below.

More about the equation of circle link is given below.

https://brainly.com/question/10618691

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