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Geometry

Conic Sections

Concept Quizzes

Conics - Circle Standard Equation
Conics - Circle General Equation
Conics - Parabola - General
Conics - Parabola - Focus and Directrix
Conics - Ellipse - General
Conics - Ellipse - Foci
Conics - Hyperbola
Conics - Discriminant
Conic Sections - Problem Solving

Challenge Quizzes

Conic Sections: Level 2 Challenges
Conic Sections: Level 3 Challenges
Conic Sections: Level 5 Challenges

Conics - Circle General Equation

What is the equation of the circle that passes through the origin, has its center on the line $x+y=4,$ and cuts the circle $x^2+y^2-6x+16y+24=0$ orthogonally?

x^2+y^2-{8}x+{2}y=0

x^2+y^2-{8}x+{4}y=0

x^2+y^2-{8}x=0

x^2+y^2-{8}x+{6}y=0

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by Brilliant Staff

Find the sum of all possible values of $b$ such that the two points $(4, 0 )$ and $(- 4, 0)$ lie on the circle $x^2 + y^2 + ax + by +c =0$ with radius $6$ .