# Using the TI-84C to find the tangent lines

In this tutorial students will learn how to use the TI-84C to graph and verify their work. The students will also learn how to convert implicit functions into explicit functions and graph using the TI-84C. The students have already found the equations of the 2 lines that are tangent to an ellipse and intersect and the point (0.4).

## Ellipse

The ellipse equation is currently in **implicit form**. To graph on the TI-84C the equations have to be entered in explicit form.

## Explicit Form

Notice that when in explicit form we have to have **two** equations. One equation for the **top half** of the ellipse and the other for the **bottom half**.

## Tangent lines

Here we also have 2 equations. The **plus sign** indicates the tangent line with the **positive slope**. The **negative sign** indicates the tangent line with the **negative slope**.

# Graphing Tool

Click on the link below to view and manipulate this graph with an online interactive graphing calculator.

# Key Skills

## Implicit Differentiation

A special case of the chain rule used when a function cannot be written as a function of x.

## Slope Intercept Form

y=mx+b Wheremis theandslopebis they-intercept.

## Trigonometry

Evaluating trigonometric functions

## Algebra

Factoring Moving terms while keeping an equation balanced Substitution Order of Operations

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