SOLUTION: If variable point (x, y) satisfies the equation x2 + y2 – 8x – 6y + 9 = 0, then range of y/x is answers is [-7/24 , infinity)

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Question 946148: If variable point (x, y) satisfies the equation x2 + y2 – 8x – 6y + 9 = 0, then range of y/x is


answers is [-7/24 , infinity)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2-8x-6y%2B9=0
%28x%5E2-8x%29%2B%28y%5E2-6y%29=-9
%28x%5E2-8x%2B16%29%2B%28y%5E2-6y%2B9%29=-9%2B16%2B9
%28x-4%29%5E2%2B%28y-3%29%5E2=16
%28y-3%29%5E2=16-%28x-4%29%5E2
y-3=+0+%2B-+sqrt%2816-%28x-4%29%29%5E2
y=-3+%2B-+sqrt%2816-%28x-4%29%29%5E2
Now you can look at the values of Z=y%2Fx
Z=%28-3+%2B-+sqrt%2816-%28x-4%29%5E2%29%29%2Fx
Since Z is now the function of only one variable, take the derivative and set it equal to zero to find the maximum value.
We'll do it in two parts because of the plus/minus value.
Z%5B1%5D=%28-3+%2B+sqrt%2816-%28x-4%29%5E2%29%29%2Fx
Z%5B1%5D has a minimum of y%2Fx=3%2F8 when x=8.
Z%5B2%5D=%28-3+-+sqrt%2816-%28x-4%29%5E2%29%29%2Fx
Z%5B2%5D has a minimum of y%2Fx=-7%2F24 when x=72%2F25.
There is no maximum so the range of y%2Fx is [-7%2F24,infinity)