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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 - Discriminant

If $A$ and $B$ are nonzero real numbers, what is the condition on $A$ and $B$ such that the equation $\frac{x^2}{A^2}+\frac{y^2}{B^2} = 1$ represents an ellipse that is not a circle?

{A}^2 + {B}^2 = 1

{A}^2 \neq {B}^2

AB<0

A = B

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by Brilliant Staff

What is the equation of the line passing through the intersection points of the following two curves: ${x}^2+{y}^2-6x-6y+17 = 0 , {x}^2+{y}^2-10x-15y+49= 0?$

{4}x+{9}y{-32}=0

{8}x+{11}y{-34}=0

{6}x+{7}y{-36}=0

{10}x+{15}y{-38}=0

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by Brilliant Staff

What is the area of the set of points in the bounded region ${x}^2 + {y}^2 -8x -8y +28 \leq 0 ?$

{4} \pi

{6} \pi

{8}

{9}

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by Brilliant Staff

If $5{x}^2+a{y}^2+4x+5y+18=0$ is an equation that represents a circle, what is the value of $a ?$

7 3 5 9

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by Brilliant Staff

Which of the following equations represents a different type of conic section than the others?

{4}{x}^2 + {8}xy + {4}{y}^2+{3}x+{3}y+{3}=0

{6}{y}^2+{2}x+{3}y+{6}=0

{4}{x}^2 + {2}x+{3}y+{2}=0

{8}{x}^2 + {10}{y}^2+{2}x+{3}y+{16}=0

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by Brilliant Staff

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