Asked by Maya
Find the equation that represents all of the points that are three times as far from (6,6) as they are from (2,0)
Answers
Answered by
Reiny
Let such a point be P(x,y)
then
√((x-6)^2 + (y-6)^2) = 3√((x-2)^2 + y^2)
square both sides and expand
x^2 - 12x + 36 + y^2 - 12y + 36 = 9x^2 - 36x + 36 + 9y^2
8x^2 + 8y^2 - 24x + 12y = 36
Sure looks like a circle.
I converted this to the standard form of a circle
(x - 3/2)^2 + (y + 3/4)^2 = 117/16
so the centre of our circle is (3/2 , -3/4) and its radius is √117/4
then
√((x-6)^2 + (y-6)^2) = 3√((x-2)^2 + y^2)
square both sides and expand
x^2 - 12x + 36 + y^2 - 12y + 36 = 9x^2 - 36x + 36 + 9y^2
8x^2 + 8y^2 - 24x + 12y = 36
Sure looks like a circle.
I converted this to the standard form of a circle
(x - 3/2)^2 + (y + 3/4)^2 = 117/16
so the centre of our circle is (3/2 , -3/4) and its radius is √117/4
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