8/21/2014 Find point(s) of the form (2a, a) that are at a distance of 7 from (-1, 4).



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8/21/21014 Solution. Using the distance formula between (2a, a) and (-1, 4), d = √(2a + 1)2 + (a – 4)2 = 7.
E
xpanding the inside and combining like terms, then squaring both sides to get rid of the √, and getting all terms to 1 side: 5a2 – 4a – 32 = 0 → a = (4 ± 4√41)/10

= (2 ± 2√41)/5. So the 2 points in the form (2a, a) are:
[(4
+ 4√41)/5, (2 + 2√41)/5] and [(4 – 4√41)/5, (2 – 2√41)/5]