Geometry

 

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.    

 

Substitute 4 for x in the equation of the circle to find the point(s) common to both curves.    

 

x² + y²  =  25    

       y²  =  25 – x²    

       y²  =  25 – 4²    

       y²  =  9    

       y  =  + 3       —>>  The curves intersect at (+4, +3) and (+4, –3)    

 

Since x=4 is a straight, vertical line, there is no horizontal component of the distance between A and B.    

 

Therefore, the distance between + 3 and – 3 is 6 units.    

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