Search the menus (Alt+/) 100% Normal text Arial 11 + BIUA ... 1 13 1 1 1 1 1 1 14 1 1 1 1 1 1 1 5 1 How can a hyperbola be graphed from its equation? Consider the equation 16x2 - 9y2 = 144 Step 1: Find the asymptotes. . It is easier to graph a hyperbola from its standard form. Therefore, divide both sides of the general form, 16%2 - 9) = 144 , by 144. The equation of the hyperbola is now: x2 y:2 9 16 This is the standard equation of a horizontal hyperbola centered at the origin. x2 9 = 0 . If the 1 is replaced with a 0, the equation then becomes: 16 (This is no longer the equation for a hyperbola, but it can help you to graph the original hyperbola.) . Use the Difference of Two Squares to factor this new equation. (: 4) (8 +4)-0 + Suggest edits . From the Zero Product Property, one can conclude that (8 4 ) - 0 ( 3 + 4 ) - 0 @ FOREST TRAIL ACADEMY Last updated 4.13.20 5 +Search the menus (Alt+/) 100% Normal text Arial - 11 + BIUA ... 1 1 12 1 1 1 1 3 1 1 1 | 1 1 1 4 1 1 1 1 1 1 1 5 1 1 1 6 1 17 1 1 1 x' - 9y = 1 x 2 gty' = 1 @ FOREST TRAIL ACADEMY Last updated 4.13.20 PRECALCULUS | ANALYTIC GEOMETRY | HYPERBOLAS, ASYMPTOTES & FACTORING y-x=1 9x - 4y = 36 READ: Read the steps for using factoring to graph a hyperbola. Graphing the hyperbola 5 How can a hyperbola be graphed from its equation? Consider the equation 16x2 - 9y2 = 144 +Search the menus (Alt+/) 100% Normal text Arial 11 + BIU A GAME. .. 1 1 1 1 1 1 1 1 1 2 1 1 1 |1 1 1 3 1 1 1 1 1 14 1 1 1 1 1 1 5 1 1 1 6 1 7 PRECALCULUS | ANALYTIC GEOMETRY | HYPERBOLAS, ASYMPTOTES & FACTORING DIRECTIONS: Complete the table using the guidelines below. Column 2: Indicate the values for A, B, C, D, E, and F by comparing the equation in Column 1 to the general equation for a conic section: Ax + Bxy + Cy + Dx + Ey + F = 0. Column 3: Evaluate B2 - 4AC and indicate if this value is greater than, less than, or equal to zero. Column 4: Use the value of B' - 4AC and the style of the equation to categorize each of the equations as representing a circle, parabola, ellipse, or hyperbola. Column 5: Find a factored form of the expression on the left-hand side of the equation. If the expression is not factorable, write cannot be factored. As an example, the first row has been completed for you. Table 1: Equations of Conics Second Degree Values for Evaluate B - Type of Conic | Factored Form Equation A, B, C, D, E, F 4AC. Section (if possible) Indicate if >,