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A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y − 4 x + 3 =0, then its radius is equal to :

  • Option 1)

    2

     

     

     

  • Option 2)

    \sqrt{5}

  • Option 3)

    \sqrt{2}

  • Option 4)

    1

 

Answers (1)

best_answer

As we learned 

 

General form of a circle -

x^{2}+y^{2}+2gx+2fy+c= 0
 

- wherein

centre = \left ( -g,-f \right )

radius = \sqrt{g^{2}+f^{2}-c}

 

 

S:x^{2}+y^{2}+2gx+2fy+c=0

C:\left ( -g,-f \right )

-f+4g+3=0

Also S passes through (2,3) and (4,5)

We get     13+4g+6f+c=0

41+8g+10f+c=0

On solving g=-2, f=-5 and simply r=2.

 


Option 1)

2

 

 

 

Option 2)

\sqrt{5}

Option 3)

\sqrt{2}

Option 4)

1

Posted by

Himanshu

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