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