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ery Precalculus: A Creative and Connected Approach RExploration 2.3.2: The Conics - Identifying Parameters Part 1. For the following problems convert the equation to standard form, create a 1 . sketch, and identify all of the critical parameters that apply. 4x2 - 8x+9y2 - 72y+112=0 2. . -4x2 + 40x+25y2-100y+100=0 3. x2 - 4x -24y+28=0 4. 4x2 - 24x-36y2 -360y+864=0 5 . 3y 2 - 4x - 6y+23=0 6. 16x2 + 16x + 9y2 + 72y+4=0 Part II. For the following problems apply your knowledge about Conics to answer the questions. 7. Two people enter a whispering gallery and want to know where they should stand so they can hear the other per- son's whisper. The gallery is 100 feet wide and the verti- cal distance from their head to the peak of the ceiling is 30 ft. 8. A hyperbolic cooling tower is 100 meters wide at the base. The most narrow section of the tower is 100 m above the ground and 40 m wide. How wide is the cooling tower at its highest point, which is 160 m above the ground? 9. A flashlight has a parabolic reflector that has a diameter of 52.25mm a depth of 23.95mm. Where should the bulb be placed for so the flashlight is optimized for a focused beam of light? Part III. Now consider, 0 = Ax2 + Cy2 + Dx + Ey + F . This is the general form of the equation for any of the conic sections (neglecting rotations). 10. How would one know which conic is represented by a given equation in this form? 11. [Extension] Put each of the conics represented in general form into the stan- dard form for the specific conic