Intersection points of circle and line when the line is parallel to y

[sunch0]

Hello, I have to find the intersection points of line AB and circle. What is the equation for x of the points when the line is parallel to the y-axis. I know the radius r, A(m,5),B(m,5+r*r) and I will try to write a program that finds the intersection points for different values of r and m, but I need a equation for calculate x for the two points.[h=1][/h]

 

[Deleted member 4993]

Hello, I have to find the intersection points of line AB and circle. What is the equation for x of the points when the line is parallel to the y-axis. I know the radius r, A(m,5),B(m,5+r*r) and I will try to write a program that finds the intersection points for different values of r and m, but I need a equation for calculate x for the two points.View attachment 7905

What are your thoughts?

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[sunch0]

The picture is just for show me how the graph i have to program should look, don't pay attention to the coordinates in the brackets. The thing is
I have a circle. The circle touches both x and y axis. And I have a line. The line is perfectly vertical and parallel to the y-axis. So the equation of circle
must be (x-r)² + (y-r)²=r² and the equation of the line must be y=x , because the line is parallel to y axis. I made a system and after replace y with x i get
x_1,2=r+/-2r² for the x coordinates and the same equation for the y coordinates of the intersection points. But it obviously does not work, because the black dots that mark the intersection point does not appear at all. So I can not understand what is the correct equation for the intersection points coordinates.

 

[mmm4444bot]

...the equation of circle must be

(x-r)² + (y-r)²=r²

and the equation of the line must be y=x , because the line is parallel to y axis.

The equation of the circle is correct, for a circle in Quadrant I, tangent to the axes.

The equation of the line is not correct.

If the vertical line is positioned m units to the right of the y-axis, then the equation of the vertical line is x=m.

Substitute x=m, in the circle's equation, and then solve for the two y-coordinates. :cool: