Algebra

 

A line and a circle intersect at A and B as shown below. Find the distance between A and B      .
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.   

 

To find the point(s) common to both functions, substitute the equal value that you know.     

 

                                                  x² + y² = 25    

you know that x=4                      4² + y² = 25    

                                                         y² = 25 – 16 = 9     

                                                         y   = +3      

and it's given that x=4    

so the points of intersection are       +4,+3 &  +4,–3   

 

so, of course, the distance between the points is 6 units    

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