P and Q are two points on the line x-y+1=0 such that each of them is 5 units far from origin. Find the co-ordinates of the points.

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Answer 1

The set of all points that are 5 units from the origin is the circle centered at (0,0) with radius 5.  

 

So, we need to solve the system of equations:

 

    y = x+1

    x² + y² = 25

 

Replace y by x+1 in the second equation to get x² + (x+1)² = 25

 

                                                                    x² + x² + 2x + 1 = 25

 

                                                                    2x² + 2x - 24 = 0

 

                                                                      x² + x - 12 = 0

 

                                                                      (x+4)(x-3) = 0

 

                                                                        x = -4 or x = 3

 

If x = -4, then y = x+1 = -3

If x = 3, then y = 4

 

The points are (-4,-3) and (3,4).