Answer:
Possible point on y-axis are ( 0 , -5 ) and ( 0 , 11 )
Step-by-step explanation:
We are given coordinate of the center of the circle ( 6 , 3 ).
The Distance from the center of the circle to the edge = 10 units.
To find: Coordinate of the point on y-axis on the edge of the circle.
Given Distance is the Length of the radius of the circle.
Radius = 10 units
We know that standard form of the coordinate of the point on the y-axis.
Coordinate of the point on the y-axis = ( 0 , y )
Also, the distance formula of the two point is given as follows,
![Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=Distance%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Now, using distance formula
we have
![\sqrt{(6-0)^2+(3-y)^2}=10](https://tex.z-dn.net/?f=%5Csqrt%7B%286-0%29%5E2%2B%283-y%29%5E2%7D%3D10)
![\sqrt{36+3^2+y^2-6y}=10](https://tex.z-dn.net/?f=%5Csqrt%7B36%2B3%5E2%2By%5E2-6y%7D%3D10)
![y^2-6y+45=100](https://tex.z-dn.net/?f=y%5E2-6y%2B45%3D100)
![y^2-6y-55=0](https://tex.z-dn.net/?f=y%5E2-6y-55%3D0)
![y^2-11y+5y-55=0](https://tex.z-dn.net/?f=y%5E2-11y%2B5y-55%3D0)
y ( y - 11 ) + 5 ( y - 11 ) = 0
( y - 11 )( y + 5 ) = 0
y - 11 = 0 ⇒ y = 11
y + 5 = 0 ⇒ y = -5
Therefore, Possible point on y-axis are ( 0 , -5 ) and ( 0 , 11 )