# Calculus – Addendum – Using the TI-84C to find the tangent lines of an ellipse through a specific point

By | November 3, 2016

# 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

$\frac {x^{2}} {4} + \frac {y^{2}} {9}=1$

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

$y= \pm \sqrt { 9 - \frac {9x^2} {4} }$

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

$y=\pm \sqrt { \frac {7} {4} }x-4$

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

Where m is the slope and b is the y-intercept.

## Trigonometry

Evaluating trigonometric functions

## Algebra

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