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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 12 Find the area of the circle.

 Dec 3, 2023
 #1
avatar+259 
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The line 3x−y=10 or y=3x−10. We use the distance formula to find the x-coordinate of each point of intersection. (3x−10)2+(3x−10)2=r2 9x2−60x+100+9x2−60x+100=r2 18x2−120x+200=r2 r2−18x2+120x−200=0

 

Since the radius is r, the x-value of A and B are r and r−6.

 

Let A=(r,3r−10) and B=(r−6,3r−26) AB=(r−r+6)2+(3r−10−3r+26)2​ AB=36+256​ AB=292​ 12=292​ 144=292 r2=144 r=12

 

The area of the circle is π(12)2=144π​ square units.

 Dec 4, 2023
 #2
avatar+33600 
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Like so:

 

 Dec 8, 2023

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