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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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