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Thread: Determining Coordinates of Two points On a Circle

  1. #1
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    Thumbs up Determining Coordinates of Two points On a Circle

    Assuming you have a circle with a radius of 2 with a line drawn exactly 1 unit away. What are the coordinates of the two points the line intersects. And how do I solve for it.

    The picture explains it well


    Determining Coordinates of Two points On a Circle-1.png
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  2. #2
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    Re: Determining Coordinates of Two points On a Circle

    Quote Originally Posted by reteach View Post
    Assuming you have a circle with a radius of 2 with a line drawn exactly 1 unit away. What are the coordinates of the two points the line intersects. And how do I solve for it.

    The picture explains it well


    Click image for larger version. 

Name:	1.png 
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ID:	37141
    The equation of a circle with centre (0, 0) and radius r is x^2+y^2=r^2.

    So find the equation of your circle and find the y values when x=1.
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  3. #3
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    Re: Determining Coordinates of Two points On a Circle

    Quote Originally Posted by reteach View Post
    Assuming you have a circle with a radius of 2 with a line drawn exactly 1 unit away. What are the coordinates of the two points the line intersects. And how do I solve for it.

    The picture explains it well Click image for larger version. 

Name:	1.png 
Views:	8 
Size:	6.0 KB 
ID:	37141
    You are looking for the points $(1,p)$ on the circle.
    Can you solve $1+p^2=4~?$
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  4. #4
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    Re: Determining Coordinates of Two points On a Circle

    Do you "see" a 30-60-90 right triangle?
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