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Conic Sections

Conics - Circle Standard Equation

What is the equation of the circle passing through the points \((0,0)\) and \((6,12)\) with center on the line \(y=x+3?\)

\( (x+6)^2+(y+3)^2=45 \) \( (x-3)^2+(y-6)^2=45 \) \( (x-6)^2+(y-3)^2=36 \) \( (x+3)^2+(y-6)^2=9 \)

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by Brilliant Staff

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?

\( x^2+(y-7)^2=58 \) \( x^2+(y-7)^2=49 \) \( x^2+(y-3)^2=49 \) \( x^2+(y-3)^2=58 \)

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by Brilliant Staff

If \((-2, -6)\) and \((8, 8)\) are two endpoints of a diameter of a circle, what is the equation of the circle?

\((x +4)^2+(y +1)^2=296 \) \((x -3)^2+(y -1 )^2=74 \) \((x -3)^2+(y -1)^2=148 \) \((x -1)^2+(y +3)^2=37 \)

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by Brilliant Staff

What is the equation of the circle tangent to the \(x\)-axis with center \((5,-1)\)?

\( (x-5)^2+(y+1)^2=1 \) \( (x+5)^2+(y-1)^2=1 \) \( (x+5)^2+(y-1)^2=12 \) \( (x-5)^2+(y+1)^2=25 \)

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by Brilliant Staff

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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by Brilliant Staff

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