I've solved some of them and the rest I don't really understand how to go about.

1. How do I find the equation of the circle if it is tangent to the line -3x+2y+5 = 0 at the point (1, -1)?

I'm stumped on this one since I don't know how I'd be able get any of the details through equations. I don't have the center point so I can't use the perpendicular distance formula/look for perpendicular line by finding the inverse of the slope (or can I? I'm not sure.)

I'm still quite confused about the circle. And I'm not really sure if the concepts I'm using are correct or not. I'm not sure if I can do this and that for this problem and that problem, but I'm slowly learning. I don't have a proper background on it since I'm just searching willy nilly.

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If you guys don't mind I have follow-ups. You don't need to give me the answers, it would help if you can explain what I'm supposed to do and how to go about doing it (Beginner level formulas for this, I guess).

1. Given circle is tangent to the line -x+y+4 = 0 at point (3, -1) and the circle's center is on the line x + 2y -3 = 0, how will I find the equation of the circle?

2.Is there a faster way to find out the equation of the circle inscribed in the triangle?

Take this for example: SOLUTION: Find the equation of the circle that is inscribed in the triangle whose sides lie on the lines 3x+y=5,x-3y=1,and x+3y=-7.

Also in that page why is it that there are only four solutions to the system. Can't the equations on the left side be negative as well?

Here's another example which is shorter but I totally don't understand how she figured out the signs.

SOLUTION: find the equation of the circle inscribed in a triangle whose sides are 3x+y-5=0, x+3y-1=0, x-3y+7=0.

Thanks for the help guys. It's greatly appreciated.