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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 - Parabola - Focus and Directrix

The above diagram shows a point $P$ on a parabola $y^2=12x$ with focus $F$ . If $l$ is a tangent line to the parabola at point $P$ , the $x$ -intercept of $l$ is $Q$ , and $\angle FPQ=36^\circ,$ what is $\angle PFQ$ in degrees?

Note: The above figure is not drawn to scale.

108 126 162 144

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by Brilliant Staff

The above diagram shows a parabola with vertex on the $y$ -axis, and directrix parallel to the $y$ -axis. If the focus of the parabola is $F=(4,6)$ , what is the equation for the parabola?

Note: The above diagram is not drawn to scale.

(y-{4})^2={12}x

(y-{6})^2={16}x

(y-{4})^2={24}x

(y-{6})^2={8}x

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by Brilliant Staff

If $y=ax+b$ is the equation for a line with slope $6$ that is a tangent line of the parabola $y^2=12x$ , what is $a+b?$

\frac{7}{2}

\frac{3}{2}

\frac{13}{2}

\frac{1}{2}

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by Brilliant Staff

Identify the focus and directrix of the parabola given by $x =-\frac{1}{28}y^{2}.$

(-7,0), x=7

(0,-7), y=7

(-7,0), x=-7

(0,-7), y=-7

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by Brilliant Staff

In the diagram above, points $P, Q,$ and $R$ lie on parabola $y^2=60x.$ If the center of gravity of $\triangle PQR$ is the focus $F$ of the parabola, what is the sum of the lengths $\overline{PF}, \overline{QF},$ and $\overline{RF}?$

Note: The figure above is not drawn to scale.

60 90 120 45

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by Brilliant Staff