Being familiar of the graph of common equation is very helpful specially when dealing with complex problem. One important application is for us to easily identify if an equation is a function or not. The graph is the soul of an equation.

General Equation:

this is also the general equations of conic sections. Where {A,B,C,D,E} are real numbers.

**Case 1: A=B **

, this is an equation of a *CIRCLE*.

Example:

But there are cases that this is an equation of an EMPTY SET.

If .

**Case 2: A & B are of the same sign but not equal.**

or , this is an equation of an *ELLIPSE*

Example:

**Case 3: A and B are of different signs. Whether A and B equal or unequal.**

, this is an equation of a HYPERBOLA

Example:

**Case 4: A=0 or B=0**

or , this is an equation of *PARABOLA*.

Example (A=0) :

Example (B=0):

**Case 5: A=0 and B=0**

, this is an equation of a *SLANT* *STRAIGHT LINE*

Example:

**Case 6. A=0, B=0,C=0**

, this is an equation of a *HORIZONTAL LINE*

Example:

**Case 7: A=0,B=0,D=0**

, this is an equation of a *VERTICAL LINE*

Example:

Practice Problems:

Direction: Identify the equation if it is a graph of parabola, hyperbola, circle, ellipse,Empty set, slant straight line, vertical line or horizontal line.

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## 1 Response

[…] Solution: This topic will help us a lot to determine the graph of an equation without actually graphing it. But since I have the power to graph it using my Geogebra tool let me show how the graph of these equations look like. […]