Circle equation

[Ana.stasia]

Determine the equation of a circle containing point A (5,2), tangent to the abscissa and having radius r = 5.

I am not sure where this translation is correct so I drew a picture. The point is that the circle touches the abscissa.

I thought about using the point where the circle touches the abscissa (x, 0), however the solution takes a different approach. It says q=r=5. S(p, q) is the center if a circle in my book.

I do not understand how q=r=5. Please explain.

 

[Dr.Peterson]

Determine the equation of a circle containing point A (5,2), tangent to the abscissa and having radius r = 5.

I am not sure where this translation is correct so I drew a picture. The point is that the circle touches the abscissa.

I thought about using the point where the circle touches the abscissa (x, 0), however the solution takes a different approach. It says q=r=5. S(p, q) is the center if a circle in my book.

I do not understand how q=r=5. Please explain.

If you are right in your translation, then "tangent" means more than you are taking it to mean. The circle not only passes through a point on the x-axis (which you call the abscissa), it must be tangent to it (merely touching), like this (where I have used a different radius, 3.25, to avoid giving away the answer):



Do you see that q = r = 3.25?

(By the way, in English, at least in my experience, the word "abscissa" refers to the x-coordinate of a point (a number), not to the x-axis (a line). But I can understand it being used your way elsewhere.)

 

[Ana.stasia]

If you are right in your translation, then "tangent" means more than you are taking it to mean. The circle not only passes through a point on the x-axis (which you call the abscissa), it must be tangent to it (merely touching), like this (where I have used a different radius, 3.25, to avoid giving away the answer):

View attachment 25697

Do you see that q = r = 3.25?

(By the way, in English, at least in my experience, the word "abscissa" refers to the x-coordinate of a point (a number), not to the x-axis (a line). But I can understand it being used your way elsewhere.)

Thank you, I solved it now.