Unit 3 Optional Review: Conics (Bartels M3H)

Last updated 10 months ago

17 questions

Instructions

Need to know:
Completing the Square (Equation of a Circle)
How to graph a parabola & label all it's key features. 
Arc Length & Sector Area
Write the equation of a parabola in standard conic form
Completing the Square (For Standard Conic Form)
Click "HINT" to reveal how to do the problem!

Completing the Square - Equation of a Circle

Given the following x^{2}+y^{2}-4x+12y-8=0, determine the equation of the circle in standard form. Then, identify the center and radius.

Standard Form: _______ 
Center:_______ 
Radius: _______ 

The endpoints of the diameter of a circle are (6,-11) and (6, 3). Find the equation of the circle.

Given the equation of a circle is (x+3)^{2}+(y-6)^{2}=25, which of the following are true? Select all that apply.

Graphing Parabolas & Their Key Features

Identify the following information. You will need to be able graph the parabola on the test!

(x+5)^{2} = -4(y-5)
Vertex:_______ 
P-value:_______ 
Focus:_______ 
Directrix:_______ 
Axis of Symmetry_______ 
Focal Width:_______ 

Write an equation of a parabola in standard conic form that has a focus at (4,-1) and directrix at y=-5.

Write an equation of a parabola in standard conic form that has a vertex of (7,-2) and a focus at (3,-2)

Rewrite the equation of the parabola given in standard conic form: y^{2}-18y+241+40x=0

True or False

Axis of Symmetry is always vertical.

The distance from directrix to vertex of parabola is always p.

The distance from directrix to focus of parabola is always 4p.

A circle with a radius of 4 has twice the area as a circle with a radius of 2

A circle with a radius of 4 has twice the circumference as a circle with a radius of 2

Vertical parabolas have no minimum or maximum value.

Horizontal parabolas have no minimum or maximum value.

Arc Length & Sector Area

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

Unit 3 Optional Review: Conics (Bartels M3H)

The endpoints of the diameter of a circle are (6,-11) and (6, 3). Find the equation of the circle.

Given the equation of a circle is (x+3)^{2}+(y-6)^{2}=25, which of the following are true? Select all that apply.

Write an equation of a parabola in standard conic form that has a focus at (4,-1) and directrix at y=-5.

Write an equation of a parabola in standard conic form that has a vertex of (7,-2) and a focus at (3,-2)

Rewrite the equation of the parabola given in standard conic form: y^{2}-18y+241+40x=0

Axis of Symmetry is always vertical.

The distance from directrix to vertex of parabola is always p.

The distance from directrix to focus of parabola is always 4p.

A circle with a radius of 4 has twice the area as a circle with a radius of 2

A circle with a radius of 4 has twice the circumference as a circle with a radius of 2

Vertical parabolas have no minimum or maximum value.

Horizontal parabolas have no minimum or maximum value.

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

Find the arc length of the circle. Leave your answer in terms of \pi

Find the area of the shaded region, round your answer to the nearest tenth.