Question:
A point P is at a distance of root of 10 from the points (4,3).Find the co-ordinates of point P ,if its ordinate is twice of its abscissa
Answer:
Given, the co-ordinates of point P whose ordinate is twice of its abscissa is (a, 2a)
Again, given, the point P is at a distance of root of 10 from the points (4,3)
=> √{(2 - a)2 + (3 - 2a)2 } = √10
=> (2 - a)2 + (3 - 2a)2 = 10
=> (4 + a2 - 4a) + (9 + 4a2 - 12a) = 10
=> 4 + a2 - 4a + 9 + 4a2 - 12a = 10
=> 13 + 5a2 - 16a = 10
=> 5a2 - 16a + 13 - 10 = 0
=> 5a2 - 16a + 3 = 0
=> 5a2 - 15a - a + 3 = 0
=>5a(a - 3) - 1(a - 3) = 0
=> (a - 3)*(5a - 1) = 0
=> a = 3, 1/5
So, 2a = 6, 3/5
Hence, the point is either (3, 6) or (1/5, 6/5)
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