SOLUTION: What is the largest value of y such that the point (8, y, 10) is 7 units away from the point (6, 9, 4)?

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Question 1092167: What is the largest value of y such that the point (8, y, 10) is 7 units away from the point (6, 9, 4)?
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the distance formula,
7%5E2=%286-8%29%5E2%2B%289-y%29%5E2%2B%284-10%29%5E2
49=4%2B36%2B%289-y%29%5E2
%289-y%29%5E2=9
9-y=0+%2B-+3
-y+=-9+%2B-+3
-y=-6 and -y=-12
y=6 and y=12
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.
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y=12

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write the equation of a sphere of the radius of 7 units and centered at the point (6,9,4):

%28x-6%29%5E2+%2B+%28y-9%29%5E2+%2B+%28z-4%29%5E2 = 7%5E2

and substitute there x = 8 and z = 10. You will get

%288-6%29%5E2+%2B+%28y-9%29%5E2+%2B+%2810-4%29%5E2 = 49,   or

2%5E2+%2B+%28y-9%29%5E2+%2B+6%5E2 = 49,   or

%28y-9%29%5E2 = 49 - 4 - 36 = 9.

Then take the square root of both sides to get

y - 9 = +/- sqrt%289%29 = +/- 3.

So, "y" may have only TWO values y = 9+3 = 12  or/and  y = 9-3 = 6.


Of them, the largest is y = 12 units.

Solved.