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Excel in math and science
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Conic Sections
Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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including olympiad champions, researchers, and professionals.
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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?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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examples, and problems from the community.
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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 \( 6 \) .
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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by Brilliant Staff
If the line \(y=ax+b\) cuts the circle \(x^2+y^2-4x+8y-29=0\) into two equal parts, then what is the value of \(2a+b ?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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by Brilliant Staff
If the circle \[x^2+y^2+ax+by+c=0\] passes through three points \[(-1,-8), (2,1), (6,-1),\] what is the value of \(a+b+c ?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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by Brilliant Staff
If the circle \(x^2+y^2+Ax+By+C=0\) passes through the origin and has the same center as the circle \(x^2+y^2-9x+8y-3=0,\) what is the value of \(A+B+C?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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by Brilliant Staff