How to Put Conics in A Ti-84 Plus Calculator
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
Graphing conic sections on your TI-84 Plus calculator is a powerful way to visualize parabolas, ellipses, circles, and hyperbolas. This guide will walk you through the process step-by-step, ensuring you get accurate and clear graphs every time.
Introduction
Conic sections are curves formed by the intersection of a plane with a cone. The four main types are parabolas, ellipses, circles, and hyperbolas. Your TI-84 Plus calculator can graph these conic sections with some setup and understanding of the equations.
Before you begin, make sure your calculator is in the correct mode. Press [MODE] and ensure that the calculator is set to "Func" (function mode) and "Rad" (radian mode).
Calculator Setup
To graph conic sections on your TI-84 Plus, you'll need to enter the equations in the correct format. The calculator uses the standard form equations for each conic section.
Standard Form Equations
- Parabola: y = ax² + bx + c
- Ellipse: (x-h)²/a² + (y-k)²/b² = 1
- Circle: (x-h)² + (y-k)² = r²
- Hyperbola: (x-h)²/a² - (y-k)²/b² = 1 or (y-k)²/a² - (x-h)²/b² = 1
To enter these equations, press [Y=] and type the equation in the appropriate line. For example, to graph a parabola, you might enter:
Y1 = 2X² - 3X + 1
Once you've entered the equation, press [GRAPH] to view the graph.
Graphing Parabolas
A parabola is a U-shaped curve that can open up, down, left, or right. To graph a parabola on your TI-84 Plus, you'll need to enter the equation in the standard form y = ax² + bx + c.
Steps to Graph a Parabola
- Press [Y=] to access the equation editor.
- Enter the equation in the form Y1 = ax² + bx + c.
- Press [GRAPH] to view the graph.
Example: To graph the parabola y = 2x² - 3x + 1, enter Y1 = 2X² - 3X + 1 and press [GRAPH].
Graphing Ellipses
An ellipse is a stretched circle. To graph an ellipse on your TI-84 Plus, you'll need to enter the equation in the standard form (x-h)²/a² + (y-k)²/b² = 1.
Steps to Graph an Ellipse
- Press [Y=] to access the equation editor.
- Enter the equation in the form Y1 = (X-h)²/a² + (Y-k)²/b² - 1.
- Press [GRAPH] to view the graph.
Example: To graph the ellipse (x-2)²/4 + (y-3)²/9 = 1, enter Y1 = (X-2)²/4 + (Y-3)²/9 - 1 and press [GRAPH].
Graphing Circles
A circle is a special type of ellipse where the width and height are equal. To graph a circle on your TI-84 Plus, you'll need to enter the equation in the standard form (x-h)² + (y-k)² = r².
Steps to Graph a Circle
- Press [Y=] to access the equation editor.
- Enter the equation in the form Y1 = (X-h)² + (Y-k)² - r².
- Press [GRAPH] to view the graph.
Example: To graph the circle (x-1)² + (y-2)² = 4, enter Y1 = (X-1)² + (Y-2)² - 4 and press [GRAPH].
Graphing Hyperbolas
A hyperbola is a curve with two branches. To graph a hyperbola on your TI-84 Plus, you'll need to enter the equation in the standard form (x-h)²/a² - (y-k)²/b² = 1 or (y-k)²/a² - (x-h)²/b² = 1.
Steps to Graph a Hyperbola
- Press [Y=] to access the equation editor.
- Enter the equation in the form Y1 = (X-h)²/a² - (Y-k)²/b² - 1 or Y1 = (Y-k)²/a² - (X-h)²/b² - 1.
- Press [GRAPH] to view the graph.
Example: To graph the hyperbola (x-2)²/4 - (y-3)²/9 = 1, enter Y1 = (X-2)²/4 - (Y-3)²/9 - 1 and press [GRAPH].
Troubleshooting
If your graph doesn't appear as expected, try these troubleshooting steps:
- Check the equation: Ensure you've entered the equation correctly in the standard form.
- Adjust the window: Press [WINDOW] and adjust the Xmin, Xmax, Ymin, and Ymax values to ensure the graph is visible.
- Clear old graphs: Press [2ND] [GRAPH] to clear any previous graphs.
- Check the mode: Ensure the calculator is in the correct mode (Func and Rad).
FAQ
Can I graph conic sections in other modes on my TI-84 Plus?
The standard form equations work best in Func mode. Switching to Parametric or Polar modes may require different equation formats.
How do I adjust the graph window for better viewing?
Press [WINDOW] and adjust the Xmin, Xmax, Ymin, and Ymax values to ensure the conic section is visible within the graph window.
Can I graph multiple conic sections at once?
Yes, you can enter multiple equations in Y1, Y2, Y3, and Y4 to graph multiple conic sections simultaneously.