Circled questions only.

In Exercises 7-12, complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle. 7. x'-12x+y'+6y=-9 8. -3x2-3y'+27y+61=0 9. x'+ y'+14x-20y-20=0 10. x3 + y'-7x-3y-1=0 11.x2 -2x+ yz +: NIW y =-1 12. 4x -16x+4y +16=0In Exercises 9-14, put the equation into standard form and identify the vertex, focus, and directrix. 9. y' -6y-36x+117 =0 10. 2x3 +4x+3y-4=0 11. x' + 6x -9y+81=0 12. 4y' + 8y+2x-10=0 13. X - 8x+6y+4=0 14. 3y' - 30y+2x+- 101 2 -=0 In Exercises 15-18, find an equation for the parabola which fits the given criteria. 15. Vertex (3,0), focus (0,0) 16. Focus (12,3), directrix x=6 17. Vertex (-8,-9); (0,0) and (-16,0) 18. The endpoints of latus rectum are are points on the curve (2,9) and (6,9) 19. The mirror in Alan's flashlight is a paraboloid of revolution. If the mirror is 8 centimeters in diameter and 4.5 centimeters deep, where should the light bulb be placed so it is at the focus of the mirror? 20. A parabolic TV antenna is constructed by taking a flat sheet of metal and bending it into a parabolic shape. If the cross section of the antenna is a parabola which is 50 centimeters wide and 30 centimeters deep, where should the receiver be placed to maximize reception? 21. A parabolic arch is constructed which is 8 feet wide at the base and 13 feet tall in the middle. Find the height of the arch exactly 2 feet in from the base of the arch