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Conic Sections

Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.

Standard Equation of a Circle

         

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 \(a+b+r ?\)

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