Geometry
Conic Sections
What is the equation of the circle passing through the points \((0,0)\) and \((6,12)\) with center on the line \(y=x+3?\)
What is the equation of the circle which passes through the two points \((-3,0)\) and \((7,4)\) and is centered at a point on the \(y\)-axis?
If \((-2, -6)\) and \((8, 8)\) are two endpoints of a diameter of a circle, what is the equation of the circle?
What is the equation of the circle tangent to the \(x\)-axis with center \((5,-1)\)?
If the circle \[x^2+y^2-8x+2y +1=0\]
has center \((a,b)\) and radius \(r,\) what is the value of \(a+b+r ?\)