8/21/2014 Find point(s) of the form (2a, a) that are at a distance of 7 from (-1, 4).
Scroll down for the solution.
8/21/21014
Solution.
Using
the distance formula between (2a,
a)
and (-1,
4), d = √(2a
+ 1)2
+ (a – 4)2
= 7.
Expanding
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]