Help please circle equation

[Ana.stasia]

Write the equation of a circle tangent to the coordinate axes, and its radius is 5.

I tried using using two points A (0,5) and B(5,0). This resulted in me getting two solutions. X2+y2=25 and the one written right at the bottom. The first solution mentioned is not in the book. Why? There are 4 soultions, I only got one right. How can I correct this?

 

[lex]

You know the centre and the radius of the particular circle you have just drawn, so you can write down its equation.
There are 4 possible pictures. Draw all 4 and write down their equations.

 

[Deleted member 4993]

Write the equation of a circle tangent to the coordinate axes, and its radius is 5.

I tried using using two points A (0,5) and B(5,0). This resulted in me getting two solutions. X2+y2=25 and the one written right at the bottom. The first solution mentioned is not in the book. Why? There are 4 soultions, I only got one right. How can I correct this?

View attachment 25726


View attachment 25728

You have correctly drawn the circle when the center is in the first quadrant. Now draw the other three positions of the centers and the associated circles and continue.....

 

[Ana.stasia]

You have correctly drawn the circle when the center is in the first quadrant. Now draw the other three positions of the centers and the associated circles and continue.....

About how I got that center of the circle is S(0,0) do I mark this as incorrect because the circle then crosses the y and x-axis rather than just touching them?

 

[lex]

Yes, is the answer to your question.
However, your page of calculation (though a nice idea) wasn't really necessary, as from your picture you can see directly that the centre of the circle is (5,5) and the radius is 5, so you can immediately write down the equation, using the fromat [MATH](x-p)^2+(y-q)^2=r^2[/MATH](If you want to prove it to yourself, you know that a line perpendicular to the tangent, going through the point of tangency, goes through the centre of the circle. I have drawn both these lines for the tangents and they both go through only one point, (5,5), so this must be the centre)!
(5,5)

Then, as Dr.Peterson says, you can simply draw the same circle (reflected) in the other quadrants (4 altogether) and again write down the centre and then the equations.
When you expand the brackets you will get the 4 answers as given.