Question 940984: Find the equation of a circle centre on the line y=2x+1 touching the y axis and passing through A(4,5)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the equation of a circle centre on the line y=2x+1 touching the y axis and passing through A(4,5)
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If by touching you mean tangent:
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Its center is equidistant from (4,5) and the y-axis.
The center is (h,k)
The distance to (4,5) = 
The distance to the y-axis = h
y = 2x + 1 --> k = 2h + 1
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Sub for k
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=64 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 4, 2.
Here's your graph:
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h = x = 4 --> center @ (4,9)
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x = 2 --> center @ (2,5)
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