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If the extremities of a diameter of a circle are (0,0) and ( a ³, 1 / a ³ ) , then the circle passes through which one of the following points?

Options

  1. A(a², 1 / a² )
  2. B( a , l / a )
  3. C( a ,- a )
  4. D(1 / a, a)

Correct answer

D. (1 / a, a)

Step-by-step solution

Given the extremities of a diameter of a circle as (0,0) and ( a ³, 1 a ) , equation of circle is (x-0) (x-a³ )+(y-0) (y- 1 a³ )=0 x²-x a³+y²- y a³ =0 x²+y²-x a³- y a³ =0 Putting x = 1 a and y = a , the equation is satisfied. Thus, the circle passes through the point ( 1 a , a ) .

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