12.3E: The Parabola (Exercises)
For the following exercises, write the equation of the parabola in standard form. Then give the vertex, focus, and directrix.
22. \(y^{2}=12 x\)
23. \((x+2)^{2}=\frac{1}{2}(y-1)\)
24. \(y^{2}-6 y-6 x-3=0\)
25. \(x^{2}+10 x-y+23=0\)
For the following exercises, graph the parabola, labeling vertex, focus, and directrix.
26. \(x^{2}+4 y=0\)
27. \((y-1)^{2}=\frac{1}{2}(x+3)\)
28. \(x^{2}-8 x-10 y+46=0\)
29. \(2 y^{2}+12 y+6 x+15=0\)
For the following exercises, write the equation of the parabola using the given information.
30. Focus at (-4,0) ; directrix is \(x=4\)
31. Focus at \(\left(2, \frac{9}{8}\right) ;\) directrix is \(y=\frac{7}{8}\)
32. A cable TV receiving dish is the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 5 feet across at its opening and 1.5 feet deep.