In the following, find the co-ordinates of the focus, axis of th

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 Multiple Choice QuestionsShort Answer Type

41. Find the co-ordinates of the centre and radii of the following circle:
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42. Find the co-ordinates of the centre and radii of the following circle:
straight x squared plus straight y squared minus 4 straight x minus 8 straight y minus 45 equals 0


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43. Find the co-ordinates of the centre and radii of the following circle:
2 straight x squared plus 2 straight y squared minus straight y equals 0



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44. Find the co-ordinates of the centre and radii of the following circle:
2 straight x squared plus 2 straight y squared minus 4 straight x minus 8 straight y minus 17 equals 0




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45. Find the co-ordinates of the centre and radii of the following circle:
space space straight x squared plus straight y squared equals straight r squared
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46. Does the indicated point lie inside, on, or outside the corresponding circles?
(1,3), space space straight x squared plus straight y squared plus 2 straight x plus 6 straight y plus 1 equals 0
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47. Does the indicated point lie inside, on, or outside the corresponding circles?
(-3, 4), straight x squared plus straight y squared equals 25
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48. Does the indicated point lie inside, on, or outside the corresponding circles?
(2, -1), space space space straight x squared plus straight y squared plus 4 straight x plus 2 straight y minus 20 equals 0
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49. In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.
straight y squared equals 10 straight x


straight y squared equals 10 straight x
It is the equation of parabola in the standard form straight y squared equals 4 ax comma space straight a greater than 0 and open towards the right.
Comparing with straight y squared space equals space 4 ax comma we have 4a = 10 rightwards double arrow space space straight a equals 5 over 2
∴  The co-ordinates of the focus S are (a, 0) left right arrow open parentheses 5 over 2 comma space 0 close parentheses
     The equation of the axis of the parabola is y = 0 (x - axis).
     The equation of directrix is x + a = 0 or space space straight x plus 5 over 2 equals 0 space or space 2 straight x plus 5 equals 0
      The length of latus rectum = <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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50. In the following, find the co-ordinates of the focus, axis of the parabola, the equation of the directrix and length of the latus rectum.
straight y squared equals negative 8 straight x
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