Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Conic Sections

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Graphing Functions

What is the center and radius of the circle indicated by the equation?

(x-2)^2+y^2=36

Possible Answers:

$(-2,0),\ r=6$

$(2,0),\ r=6$

$(-2,0),\ r=36$

$(2,0),\ r=36$

Correct answer:

$(2,0),\ r=6$

Explanation:

A circle is defined by an equation in the format (x-h)^2+(y-k)^2=r^2 .

The center is indicated by the point (h,k) and the radius .

In the equation (x-2)^2+(y)^2=36=6^2 , the center is (2,0) and the radius is .

Report an Error

Example Question #1 : Pre Calculus

What is the shape of the graph indicated by the equation?

$\frac{x^{2}}{16}+\frac{y^2}{4}=1$

Possible Answers:

Circle

Parabola

Ellipse

Hyperbola

Correct answer:

Ellipse

Explanation:

An ellipse has an equation that can be written in the format $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$ . The center is indicated by (h,k) , or in this case (0,0) .

Report an Error

Example Question #2 : Pre Calculus

A conic section is represented by the following equation:

$\small -4x^{2} + 15y^{2} + 343 =0$

What type of conic section does this equation represent?

Possible Answers:

Parabola

Hyperbola

Circle

Ellipse

Correct answer:

Hyperbola

Explanation:

The simplest way to know what kind of conic section an equation represents is by checking the coefficients in front of each variable. The equation must be in general form while you do this check. Luckily, this equation is already in general form, so it's easy to see. The general equation for a conic section is the following:

$Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0$

Assuming the term Bxy is 0 (which it usually is):

If A equals C, the equation is a circle.
If A and C have the same sign (but are not equal to each other), the equation is an ellipse.
If either A or C equals 0, the equation is a parabola.
If A and C are different signs (i.e. one is negative and one is positive), the equation is a hyperbola.

Report an Error

Example Question #3 : Pre Calculus

A conic section is represented by the following equation:

$\frac{(x-3)^{2}}{4}-\frac{(y+2)^{2}}{9}=1$

Which of the following best describes this equation?

Possible Answers:

horizontal hyperbola with center of (3,-2) and asymptotes with slopes of $\frac{3}{2}$ and $-\frac{3}{2}$

vertical ellipse with center (-3,2) and a major axis length of

vertical hyperbola with center (3, -2) and asymptotes with slopes of $\frac{2}{3}$ and $-\frac{3}{2}$

horizontal hyperbola with center (3,-2) and asymptotes with slopes of $\frac{2}{3}$ and $-\frac{2}{3}$

vertical parabola with vertex (-3, 2) and a vertical stretch factor of

Correct answer:

horizontal hyperbola with center of (3,-2) and asymptotes with slopes of $\frac{3}{2}$ and $-\frac{3}{2}$

Explanation:

First, we need to make sure the conic section equation is in a form we recognize. Luckily, this equation is already in standard form:

$\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$

The first step is to determine the type of conic section this equation represents. Because there are two squared variables ( $x^{2}$ and $y^{2}$ ), this equation cannot be a parabola. Because the coefficients in front of the squared variables are different signs (i.e. one is negative and the other is positive), this equation must be a hyperbola, not an ellipse.

In a hyperbola, the squared term with a positive coefficient represents the direction in which the hyperbola opens. In other words, if the $x^{2}$ term is positive, the hyperbola opens horizontally. If the $y^{2}$ term is positive, the hyperbola opens vertically. Therefore, this is a horizontal hyperbola.

The center is always found at (h, k) , which in this case is (3, -2) .

That leaves only the asymptotes. For a hyperbola, the slopes of the asymptotes can be found by dividing by (remember to always put the vertical value, , above the horizontal value, ). Remember that these slopes always come in pairs, with one being positive and the other being negative.

In this case, is 3 and is 2, so we get slopes of $\frac{3}{2}$ and $-\frac{3}{2}$ .

Report an Error

Example Question #2 : Pre Calculus

Find the vertex $\left ( x,y \right )$ for a parabola with equation

y=3x^2-6x+1

Possible Answers:

$\left ( 1,3 \right )$

$\left ( 1,1 \right )$

$\left ( 2,-1 \right )$

$\left ( 1,-2 \right )$

$\left ( 1,2 \right )$

Correct answer:

$\left ( 1,-2 \right )$

Explanation:

For any parabola of the form ax^2+bx+c , the -coordinate of its vertex is

$x = \frac{-b}{2a}$

So here, we have

$x=\frac{-(-6))}{2(3)}$

We plug this back into the original equation to find :

y = 3(1)^2-6(1)+1

Report an Error

Example Question #4 : Pre Calculus

What is the minimal value of

2x^2+16x-7

over all real numbers?

Possible Answers:

No minimum value.

Correct answer:

Explanation:

Since this is an upwards-opening parabola, its minimum value will occur at the vertex. The -coordinate for the vertex of any parabola of the form

y = ax^2 + bx+c

is at

$x = \frac{-b}{2a}$

So here,

$x = \frac{-b}{2a}$

$= \frac{-(16)}{2(2)}$

= -4

We plug this value back into the equation of the parabola, to find the value of the function at this .

y = 2(-4)^2 + 16(4) - 7

=-39

Thus the minimal value of the expression is .

Report an Error

View Tutors

Nicole
Certified Tutor

Liberty University, Bachelor of Science, Psychology. Liberty University, Master of Arts, Mental Health Counseling.

View Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

View Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in San Francisco-Bay Area, Spanish Tutors in San Francisco-Bay Area, Calculus Tutors in Chicago, Biology Tutors in Seattle, GMAT Tutors in San Diego, GRE Tutors in Phoenix, GRE Tutors in Philadelphia, Statistics Tutors in Chicago, GMAT Tutors in Houston, ACT Tutors in Philadelphia

Popular Courses & Classes

LSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Boston, GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Philadelphia, MCAT Courses & Classes in San Diego, ACT Courses & Classes in Houston, ISEE Courses & Classes in Houston, SAT Courses & Classes in San Diego, GRE Courses & Classes in Denver, GMAT Courses & Classes in Miami

Popular Test Prep

SAT Test Prep in Chicago, GRE Test Prep in Denver, GMAT Test Prep in Dallas Fort Worth, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Seattle, SAT Test Prep in Philadelphia, GRE Test Prep in Los Angeles, MCAT Test Prep in Chicago, ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

High School Math : Conic Sections

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Graphing Functions

Example Question #1 : Pre Calculus

Example Question #2 : Pre Calculus

Example Question #3 : Pre Calculus

Example Question #2 : Pre Calculus

Example Question #4 : Pre Calculus

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: