SOLUTION: Find the equation of a circle centre on the line y=2x+1 touching the y axis and passing through A(4,5)

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:
--
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
---

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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