Graphing and Translating Ellipses Solutions

• To graph an ellipse on the coordinate plane, mark these items:

  •    center    

  •    vertices   
  •    co-vertices   
• Optionally, you can sketch vertical and horizontal    tangent lines     to help make your graph more accurate.

  • A tangent line is a line that touches a curve at    exactly one point    .

  • When drawing tangent lines for ellipses, use    dashed     lines.

• An ellipse is transformed by    translating     it horizontally or vertically.

  • Horizontal translations move the center    left or right    .

  • Vertical translations move the center    up or down    .

Example 3

Graph. Describe the similarities and differences between the graphs.

$P:\frac{x^2}{49}+\frac{y^2}{49}=1 Q:\frac{x^2}{81}+\frac{y^2}{49}=1$

Note

You can write a circle in standard form of an ellipse or clear the denominator to write it in the standard form of a circle: $x^2+y^2=49$.

Example 4

Write the equation of an ellipse with a vertical major axis length of 10 units and a minor axis of 8 units that is translated right 5 units and down 3 units from the origin, then graph.