SOLUTION: Find the coordinates of all points that are on the line x=y and are five units from (3,-1).

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Question 517509: Find the coordinates of all points that are on the line x=y and are five units from (3,-1).
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find the coordinates of all points that are on the line x=y and are five units from (3,-1).
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It's the 2 points of intersection of the line and a circle of radius 5 centered at (3,-1).
The circle is
x = y


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=136 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.91547594742265, -1.91547594742265. Here's your graph:

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x,y = 1 + sqrt(8.5)
x,y = 1 - sqrt(8.5)
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