Choose the correct statement about two circles whose equations are given below:
x² + y² - 10x - 10y + 41 = 0
x² + y² - 22x - 10y + 137 = 0
Choose the correct statement about two circles whose equations are given below:
x² + y² - 10x - 10y + 41 = 0
x² + y² - 22x - 10y + 137 = 0
Option 1 -
Circles have no meeting point
Option 2 -
Circles have two meeting points
Option 3 -
Circles have only one meeting point
Option 4 -
Circles have same centre
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1 Answer
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Correct Option - 3
Detailed Solution:Circle 1: x² + y² - 10x - 10y + 41 = 0
Center C? = (5,5).
Radius r? = √ (5² + 5² - 41) = √ (25+25-41) = √9 = 3.Circle 2: x² + y² - 22x - 10y + 137 = 0
Center C? = (11,5).
Radius r? = √ (11² + 5² - 137) = √ (121+25-137) = √9 = 3.Distance between centers d (C? , C? ) = √ (11-5)² + (5-5)²) = √ (6²) = 6.
Sum of radii r? + r? = 3 + 3 = 6.
Since the distance between the centers is equal to the sum of their radii, the circles touch externally at one point.
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