Classifying a Conic Section (in Standard Form)
To classify a conical section, remember the standard form of each.
[include_netrun_products_block from-products="product/6-virginia-sol-grade-3-math-practice-tests/" product-list-class="bundle-products float-left" product-item-class="float-left" product-item-image-container-class="p-0 float-left" product-item-image-container-size="col-2" product-item-image-container-custom-style="" product-item-container-size="" product-item-add-to-cart-class="btn-accent btn-purchase-ajax" product-item-button-custom-url="{url}/?ajax-add-to-cart={id}" product-item-button-custom-url-if-not-salable="{productUrl} product-item-container-class="" product-item-element-order="image,title,purchase,price" product-item-title-size="" product-item-title-wrapper-size="col-10" product-item-title-tag="h3" product-item-title-class="mt-0" product-item-title-wrapper-class="float-left pr-0" product-item-price-size="" product-item-purchase-size="" product-item-purchase-wrapper-size="" product-item-price-wrapper-class="pr-0 float-left" product-item-price-wrapper-size="col-10" product-item-read-more-text="" product-item-add-to-cart-text="" product-item-add-to-cart-custom-attribute="title='Purchase this book with single click'" product-item-thumbnail-size="290-380" show-details="false" show-excerpt="false" paginate="false" lazy-load="true"]
Conic Section can be represented by a cross-section of a plane cutting through a cone.
Related Topics
- Standard Form of a Circle
- How to Write the Equation of Parabola
- Equation of Each Ellipse and Finding the Foci, Vertices, and Co– Vertices of Ellipses
- Hyperbola in Standard Form and Vertices, Co– Vertices, Foci, and Asymptotes of a Hyperbola
Step by Step Guide to Classifying a Conic Section
The formula for four basic conic sections are provided in table below:
| Conic section | Standard form of equation |
| Parabola | \((x- h)^2= 4p(y-k)\), \((y+k)^2= 4p(x-h)\) |
| Circle | \((x- h)^2+( y-k)^2=r^2\) |
| Ellipse | \(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\), \(\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1\) |
| Hyperbola | \(\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\), \(\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\) |
- For identify a conic section Group \(x\) and \(y\) variables together, then convert \(x\) and \(y\) to square form.
Classifying a Conic Section – Example 1:
Write this equation in standard form: \(x^2+y^2+12x=-11\)
Solution:
Group \(x\)-variables and \(y\)-variables together: \((x^2+12x+36)+y^2=-11\)
Convert \(x\) to square form: \((x^2+12x+36)+y^2=-11+36\) → \((x^2+12x+36)+y^2=25\)
Original price was: $109.99.$54.99Current price is: $54.99.
Then: \((x+6)^2+y^2=5^2\), its a circle.
Exercises for Classifying a Conic Section
Write teach equation in standard form.
- \(\color{blue}{x^2+y^2+6y=7}\)
- \(\color{blue}{x^2-y^2+2x+10y=124}\)
- \(\color{blue}{x^2+2x-4y=-25}\)
- It’s a circle: \(\color{blue}{x^2+(y+3)^2=16}\)
- It’s a hyperbola: \(\color{blue}{\frac{(x-(-1))^2}{10^2}-\frac{y-5}{10^2}=1}\)
- It’s parabola: \(\color{blue}{(x-(-1))^2=4(y-6)}\)
Original price was: $109.99.$54.99Current price is: $54.99.
Related to This Article
More math articles
- How to Graph Absolute Value Function?
- How to Teach the GED Math Effectively: A Complete Guide!
- 15 Surprising Things You Need Math For
- How to Understand Vectors: Vectors in Two Dimensions
- Algebra Puzzle – Challenge 58
- Why Math Matters in Your Future IT Career?
- How to Solve Irrational Functions?
- How to Learn Properties of Logarithms
- Full-Length ISEE Upper Level Math Practice Test
- How to Prepare for the PSAT 8/9 Math Test?
What people say about "Classifying a Conic Section (in Standard Form) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.