Question

the set of circles passing through the origin (0,0). is this set infinite or finite please give explanation ​

Answer 1

Answer:

it is an infinite set.

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Answer 2

Given : the set of circles passing through the origin (0,0).

To Find : is this set infinite or finite  

Solution:

Finite Set has limited number of elements which are countable

Infinite Set has unlimited number of elements and hence uncountable

Equation of a circle is given by

(x - h)² + (y - k)² = r²

(h , k) center  , r = radius

Substituting  x= 0 an y = 0  as circle passes through origin

Hence h² + k² = r²

There Exist infinite values which satisfy this  

as h ∈ (-∞ , ∞)  and k  ∈ (-∞ , ∞)   and accordingly r ∈ (0 , ∞)

Hence infinite circles exist

So Set is INFINITE

the set of circles passing through the origin (0,0)  is INFINITE

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