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 Identify and Graph a Conic Write x 2 + y 2 + 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. x 2 + y 2 + 4x - 6y = -4 Original equation (x 2 + 4x + ■) + (y 2 - 6y + ■) = -4 Isolate terms. (x 2 + 4x + 4) + (y 2 - 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 = r 2 , 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. 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 . [ -12.6, 12.6] scl: 1[-6.2, 6.2] scl: 1 Exercises Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. 1. x 2 - y 2 + 8x = 16 2. y 2 - 2x 2 - 16 = 0 3. x 2 + 2y 2 = 2x + 8 4. x 2 - 8y + y 2 + 11 = 0 5. 9y 2 + 18y = 25x 2 + 216 6. x 2 + 4y 2 + 2x - 24y + 33 = 0 7. 3x 2 + 4y 2 + 8y = 8 8. x 2 + 4y 2 - 11 = 2(4y - x) 9. 6x 2 - 24x - 5y 2 - 10y - 11 = 0 10. 25y 2 + 9x 2 - 50y - 54x = 119 Objective Graph conic sections using a graphing calculator. Casio FX-9750G