If the circles x 2 + y 2 + 2ax + 2by + c = 0 and x 2 + y 2 + 2bx + 2ay + c = 0 where c > 0, have exactly one point in common then the value of \(\frac{(a+b)^{2}}{2 c}\) is :

Circles

Grade None

Question:

If the circles x2 + y2 + 2ax + 2by + c = 0 and x2 + y2 + 2bx + 2ay + c = 0 where c > 0, have exactly one point in common then the value of \(\frac{(a+b)^{2}}{2 c}\) is :

1/2

1

\(\sqrt{2}\)

2

Step-by-Step Solution

Key Concept: Two circles with equal radii have exactly one point in common only when they touch externally, meaning the distance between their centers equals the sum of their radii.

1

Correct Answer: B

Question:

Step-by-Step Solution

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