Conic Sections and Completing the Square

Conic Sections and Completing the Square

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to recognize different types of conic sections from equations by using the method of completing the square. It starts with an introduction to conic sections and then provides a detailed example of identifying a circle by completing the square. The tutorial continues with another example, demonstrating how to identify an ellipse using the same method. The video emphasizes the importance of recognizing coefficients and signs in equations to determine the type of conic section represented.

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23 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in recognizing a conic section from an equation?

Graph the equation

Identify the highest degree term

Complete the square

Factor the equation

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What operation is performed to both sides of the equation to maintain equality when completing the square?

Add the same number

Subtract the same number

Divide by the same number

Multiply by the same number

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the center of the circle represented by the equation x^2 + y^2 + 4y = -30?

(0, 2)

(0, -2)

(2, 0)

(-2, 0)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you determine the radius of a circle from its equation in standard form?

Square the constant on the right side

Double the constant on the right side

Take the square root of the constant on the right side

Halve the constant on the right side

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of a circle in standard form?

x^2 + y^2 = r^2

(x - h)^2 + (y - k)^2 = r^2

(x - h)^2/a^2 + (y - k)^2/b^2 = 1

ax^2 + by^2 = c

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the radius of a circle with the equation x^2 + y^2 + 4y = -30 after completing the square?

14

√14

28

√28

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of the constant term in the standard form of a circle's equation?

It represents the circumference

It represents the radius squared

It represents the diameter

It represents the area

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