Circle equation, got two, only one right

A

Ana.stasia

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Determine the equation of the circle, which contains points A (2,4) and B (6,8) and touches the abscissa.

I got two answers for the center of the circle (6,4) which is correct and (-10,20) which I thought was correct because It worked with points A, B, however, It didnt work with C. Where did I go wrong to get the second option?

IMG_20210314_192326.jpg
 
Beer soaked ramblings follow.
Ana.stasia said:
Yes, I saw that I got the point wrong and that it is possible to create a circle with the center (-10,20) but the (-10, 20) is not written in the solution in the book. Could there be a reason other than that the book is wrong?
Click to expand...
Probably.
You've been posting unusual precalculus problems lately and I was wondering what book (name and author) you are using.
 
Draw the line line segment from A (2,4) to B (6,8). The midpoint of A and B is (4,4). Now at (4,4) draw a perpendicular line to AB. Every point on that line can serve as the center of a circle that contains A (2,4) and B (6,8). Where does that point cross the abscissa? That will give you the three points on a circle.

Now armed with 3 points on a circle how do you find the center of the circle?
 
Ana.stasia said:
Yes, I saw that I got the point wrong and that it is possible to create a circle with the center (-10,20) but the (-10, 20) is not written in the solution in the book. Could there be a reason other than that the book is wrong?
Click to expand...
You work looks good; you just checked the center (-10,20) instead of the point of tangency, (-10,0). I think that is what you are saying.

Are you saying that the book gives only the one solution for the center, (6, 4), or something else? What does the book actually say?

If they didn't state an additional condition, and showed only one solution, then they are wrong.
 
jonah2.0 said:
Beer soaked ramblings follow.

Probably.
You've been posting unusual precalculus problems lately and I was wondering what book (name and author) you are using.
Click to expand...

I am pretty sure it isn't translated in english.
The author is Mr Vene T. Bogoslavovn and the name of the book in english would be "a collection of solved math problems"; there is 4 books.
 
Jomo said:
Draw the line line segment from A (2,4) to B (6,8). The midpoint of A and B is (4,4). Now at (4,4) draw a perpendicular line to AB. Every point on that line can serve as the center of a circle that contains A (2,4) and B (6,8). Where does that point cross the abscissa? That will give you the three points on a circle.

Now armed with 3 points on a circle how do you find the center of the circle?
Click to expand...

System of equations.
 
Dr.Peterson said:
You work looks good; you just checked the center (-10,20) instead of the point of tangency, (-10,0). I think that is what you are saying.

Are you saying that the book gives only the one solution for the center, (6, 4), or something else? What does the book actually say?

If they didn't state an additional condition, and showed only one solution, then they are wrong.
Click to expand...

Yes, the book only listed the solution with (6,4) as cordinates while I got (-10,20) too.
 
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