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Statement I : The only circle having radius \sqrt{10} and a diameter along line 2x+y=5 is x^{2}+y^{2}-6x+2y=0.

Statement II : 2x+y=5 is a normal to the circle x^{2}+y^{2}-6x+2y=0.

Option: 1

Statement I is false ;Statement II is true.


Option: 2

Statement I is true ; Statement II is true; Statement II is a correct explanation for statement I.


Option: 3

Statement I is true; Statement II is false.


Option: 4

Statement I is true;Statement II is not a correct ecplanation for statement I.


Answers (1)

best_answer

\\\mathrm{equation \;of\; circle\;\; x^{2}+y^{2}-6 x+2 y=0}\\\text{center }(3,-1)

Given equation of line is 2x + y = 5

The line passes through the point (3, -1) 

Therefore line passes through the centre. The given line is normal to the circle.

Thus statement-  2 is true, but statement-1 is not true as there are infinite circle according to the given conditions. 

Posted by

Ritika Kankaria

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