Find the points on x- axis which are at a distance of 2√5 units from the point (7, -4) . How many such points are there?

Asked by SANDRA SAJI | 2nd Feb, 2017, 09:53: PM

Expert Answer:

begin mathsize 16px style Let space the space point space on space the space straight x minus axis space be space left parenthesis straight a comma 0 right parenthesis.
So comma space using space distance space formula comma space we space get
2 square root of 5 equals square root of left parenthesis 7 minus straight a right parenthesis squared plus left parenthesis negative 4 minus 0 right parenthesis squared end root
Squaring space both space sides comma space we space get
20 equals left parenthesis 7 minus straight a right parenthesis squared plus left parenthesis negative 4 minus 0 right parenthesis squared
rightwards double arrow 49 minus 14 straight a plus straight a squared plus 16 equals 20
rightwards double arrow straight a squared minus 14 straight a plus 45 equals 0
rightwards double arrow left parenthesis straight a minus 9 right parenthesis left parenthesis straight a minus 5 right parenthesis equals 0
rightwards double arrow straight a equals 9 space or space straight a equals 5
So comma space the space points space are space left parenthesis 9 comma 0 right parenthesis space and space left parenthesis 5 comma 0 right parenthesis.
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Answered by Rebecca Fernandes | 3rd Feb, 2017, 09:32: AM

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