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If the smallest radius of a circle passing through the intersection of x 2 + y 2 + 2x = 0 and x - y = 0 , is r then value of 10r 2 is equal to?

If the smallest radius of a circle passing through the intersection of x+ y2  + 2x = 0 and x - y = 0 , is r then value of 10r2  is equal to?

Grade:12

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
Circle which have smallest radius willbhave that chord as diameter 
 
Hence
 
Find the points of intersection and then length this will be the diameter.
 
2 x² + 2x = 0
 
Hence
 
x = 0 and -1
 
Hence
 
Points are (0,0) and (-1, -1)
 
Hence diameter = sqrt (2)
 
Radius = sqrt (2) /2 = 1 /sqrt (2)
 
Hence 10r² = 10/2 = 5

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