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)?

Algebra.Com
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)   (Show Source): You can put this solution on YOUR website!
Use the distance formula,





and
and
.
.
.
Answer by ikleyn(52797)   (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):

 = 

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

 = 49,   or

 = 49,   or

 = 49 - 4 - 36 = 9.

Then take the square root of both sides to get

y - 9 = +/-  = +/- 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.





RELATED QUESTIONS

The point (5,y) is five units away from the point (2,70). What are the two possible... (answered by math-vortex)
The point (x, y) is on the x-axis and is 6 units away from the point (1, 4), find x and... (answered by ewatrrr)
Point P (-4,a) and point (4,b) are both 5 units away from the origin. What's the maximum... (answered by josgarithmetic)
a b c d e f g h i j k l m n o p q r (answered by ewatrrr)
The point (a,b) is 5 units away from the point (6,3), and (a,b) lies on the line 5x - 4y... (answered by KMST)
Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the... (answered by robertb)
Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the... (answered by stanbon)
Find the coordinates of a point(x,y) on the line y=x+4 which is the root of 106 units... (answered by solver91311)
The point is in the second quadrant and is 4 units away from the y-axis and twice as far (answered by jim_thompson5910,MathLover1)