# Calculus – Addendum – Find 2 tangent lines to an ellipse that intersect at a point not on the graph

By | November 2, 2016

# Addendum – Find the tangent line equations

In this tutorial the students will revisit a previous tutorial where we found the equation to 2 tangent lines.  The problem is that the equations are in a more complex form.  The students will simplify the tangent line equations and verify their results using an online graphing calculator.

In the effort to simplify the equations the students will learn how to …

• Find common denominators
• Subtract fractions
• Rationalize

$y-4=\frac {4 - \frac {9} {4}} {\pm \sqrt {\frac {7}{4}}}x$ becomes $y={\pm\sqrt {\frac {7}{4}}}x+4$

# Graphing Tool

Click on the image below to work on equations for this problem with an interactive online 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