Graphing Technology Lab

Identifying and Graphing Conic Sections

You can use a Casio FX-9750G application to make graphing conics on your graphing calculator without having to solve for y.

EXAMPLE 1

EXAMPLE Identify and Graph a Conic

Write x2 + y2 + 4x - 6y = -4 in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.

Step 1 Write in standard form.

x2 + y2 + 4x - 6y = -4 Original equation (x2 + 4x + �) + (y2 - 6y + �) = -4 Isolate terms. (x2 + 4x + 4) + (y2 - 6y + 9) = -4 + 4 + 9 Complete the square. (x + 2)2 + (y - 3)2 = 9 Write as perfect squares.

Step 2 Identify the conic.

The equation is in the form (x - h)2 + (y - k)2 = r2, so the conic is a circle.

Step 3 Graph the equation.

Use the CONICS menu to graph the circle.

Press MENU 9 to select Conics.

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Then use to select the equation for a circle. Press EXE .

Set the viewing window.

KEYSTROKES: SHIFT F3 12.6 EXE 12.6

EXE 6.2 EXE 6.2 EXE EXE

Enter the values for H, K, and R: press 2 EXE 3 EXE 3

EXE F6 .

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[-12.6, 12.6] scl: 1[-6.2, 6.2] scl: 1

EXAMPLE 1

ExercisesWrite each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation.

1. x2 - y2 + 8x = 16 2. y2 - 2x2 - 16 = 0

3. x2 + 2y2 = 2x + 8 4. x2 - 8y + y2 + 11 = 0

5. 9y2 + 18y = 25x2 + 216 6. x2 + 4y2 + 2x - 24y + 33 = 0

7. 3x2 + 4y2 + 8y = 8 8. x2 + 4y2 - 11 = 2(4y - x)

9. 6x2 - 24x - 5y2 - 10y - 11 = 0 10. 25y2 + 9x2 - 50y - 54x = 119

Objective Graph conic sections using a graphing calculator.

Casio FX-9750G

Casio_661_C010L6B_888482.indd 661 8/17/09 1:36:34 PM