Asked by Tsunayoshi
Find the equation of the graph of all points such that the difference of their distances from (10,0) and (2,0) is always 1.
Answers
Answered by
Damon
hyperbola centered at x =12/2 = 6
hits x axis at (5.5 , 0) and (6.5 , 0)
(x-6)^2/a^2 - y^2/b^2 = 1
2 a = 1
a = 1/2
a^2 = 1/4
4 (x-6)^2 - y^2/b^2 = 1
center to either focus = 4 =sqrt(a^2+b^2)
so
16 = 1/4 + b^2
b^2 = 16 - 1/4 = 63/4
4(x-6)^2 - 4y^2/63 = 1
(x-6)^2 - y^2/63 = 1/4
hits x axis at (5.5 , 0) and (6.5 , 0)
(x-6)^2/a^2 - y^2/b^2 = 1
2 a = 1
a = 1/2
a^2 = 1/4
4 (x-6)^2 - y^2/b^2 = 1
center to either focus = 4 =sqrt(a^2+b^2)
so
16 = 1/4 + b^2
b^2 = 16 - 1/4 = 63/4
4(x-6)^2 - 4y^2/63 = 1
(x-6)^2 - y^2/63 = 1/4
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