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What is the length of the line x-2y equals 8 that intersects xy equals 24 at two points showing all work?
Wiki User
∙ 10y ago
x - 2y = 8 => x = 2y + 8
Substituting in the other equation,
(2y + 8)*y = 24
or (y + 4)*y = 12
y2 + 4y - 12 = 0
(y + 6)*(y - 2) = 0
So that y = -6 or y = 2
Now xy = 24
so y = 6 => x = 24/6 = 4
and y = -2 => x = 24/(-2) = -12
So the two points of intersection are (4, 6) and (-2, -12)
The length of the line joining them is
sqrt[(4 + 2)2 + (6 + 12)2] = sqrt[36 + 324] = sqrt[360] = 6*sqrt(10) = 18.97 approx.
Another possible answer:-
x-2y = 8 => x = 2y+8
xy = 24 => y(2y+8) = 24 => y2+4y-12 = 0 by dividing all terms by 2
Using the quadratic equation formula: y = -6 and y = 2
By substitution the points intersect at: (-4, -6) and (12, 2)
Length of the line is square root of: (-4-12)2+(-6-2)2 = 17.889 rounded to 3 decimal places
Wiki User
∙ 10y ago
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