# Classifying a Conic Section (in Standard Form)

To classify a conical section, remember the standard form of each. Conic Section can be represented by a cross-section of a plane cutting through a cone.

## Step by Step Guide to Classifying a Conic Section

The formula for four basic conic sections are provided in table below:

• 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: $$(x^2+12x+36)+y^2=-11+36$$ $$(x^2+12x+36)+y^2=25$$

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: $$\color{blue}{(x-(-1))^2=4(y-6)}$$

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