SOLUTION: Find all points on the y-axis that are a distance 7 from P(5, 9).

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Question 992588: Find all points on the y-axis that are a distance 7 from P(5, 9).
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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Point(x%5B2%5D,y%5B2%5D)=(5,9)
Point(x%5B1%5D.y%5B1%5D)=(0,y)
d=distance=7
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d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29
7=sqrt%28%285-0%29%5E2%2B%289-y%29%5E2%29
7=sqrt%285%5E2%2B%289-y%29%5E2%29
49=25%2B%289-y%29%5E2
24=y%5E2-18y%2B81
0=y%5E2-18y%2B57
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B-18y%2B57+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-18%29%5E2-4%2A1%2A57=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+96+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+96+%29%29%2F2%5C1+=+13.8989794855664
y%5B2%5D+=+%28-%28-18%29-sqrt%28+96+%29%29%2F2%5C1+=+4.10102051443364

Quadratic expression 1y%5E2%2B-18y%2B57 can be factored:
1y%5E2%2B-18y%2B57+=+1%28y-13.8989794855664%29%2A%28y-4.10102051443364%29
Again, the answer is: 13.8989794855664, 4.10102051443364. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B57+%29

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y=4.1 or 13.9
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ANSWER: There are two points: (0,4.1) and (0,13.9)
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