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
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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


space space straight y squared equals negative 8 straight x
It is the equation of a parabola in the standard form straight y squared equals negative 4 ax comma space straight a greater than 0 and open towards the left.

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The focus is straight S space left parenthesis negative straight a comma space 0 right parenthesis space left right arrow space left parenthesis negative 2 comma space 0 right parenthesis
The equation of axis of parabola is y = 0 (x-axis).
The equation of directrix is x - a = 0 or x - 2 = 0
The length of latus rectum = 4a = 4 space cross times space 2 equals 8
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