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The line y = 3x - 10 intersects a circle centered at the origin at A and B.  We know the length of chord AB is \(10\). Find the area of the circle.

 Apr 21, 2022
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If we draw a radius bisecting this  chord it will do so at right angles

 

The distance from the origin to this line is  given by

 

  l 3(0) - 1(0)  - 10 l    /  [sqrt 3^2 + 1^2 ]   =    10   / sqrt  10  =  sqrt 10

 

So    we can form  a right triangle   with  ......   r = the hypotenuse   and legs of 5  and sqrt (10)

 

r^2  =  5^2  + (sqrt 10)^2  =  25 + 10  =  35

 

Area of the circle =  pi * r^2  = pi * 35  =   35 pi  units^2

 

 

cool cool cool

 Apr 21, 2022

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