# 12.3E: The Parabola (Exercises)

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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.

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