Brilliant

Home Courses Today

Excel in math and science.

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

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 - Ellipse - General

Let $(m,n)$ be the point at which a line is tangent to the ellipse $\displaystyle{\frac{x^2}{16}+\frac{y^2}{100}=1}.$ If this line has $x$ -intercept $A=(a,0)$ and $y$ -intercept $B=(0,b),$ where $a$ and $b$ are positive, what is the minimum value of $ab?$

78 80 82 84

Show explanation

View wiki

by Brilliant Staff

The ellipse $\displaystyle{\frac{x^2}{8}+\frac{y^2}{17}=1}$ and the line $y=2x - k$ intersect at exactly two distinct points. What is the range of the constant $k?$

-\sqrt{{47}}<k< \sqrt{{47}}

-\sqrt{{53}}<k< \sqrt{{53}}

-\sqrt{{49}}<k< \sqrt{{49}}

-\sqrt{{51}}<k< \sqrt{{51}}

Show explanation

View wiki

by Brilliant Staff

Find the equation of the tangent line to the ellipse $1x^2+y^2=53$ at the point $(2,7)$ on the ellipse.

2x-7y=53

2x-7y=51

2x+7y=51

2x+7y=53

Show explanation

View wiki

by Brilliant Staff

In the above diagram, a rectangle $ABCD$ is inscribed in the ellipse $\displaystyle{\frac{x^2}{36}+\frac{y^2}{100}=1}.$ What is the maximum area of rectangle $ABCD?$

Note: The above diagram is not drawn to scale.

122 118 124 120

Show explanation

View wiki

by Brilliant Staff

Find the maximum area of the rectangle which is inscribed in the ellipse $\frac{x^{2}}{5^{2}}+\frac{y^{2}}{2^{2}} = 1.$

40 20 10 30

Show explanation

View wiki

by Brilliant Staff

Problem Loading...

Note Loading...

Set Loading...