The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is

  • Option 1)

    x^{2}+y^{2}=9a^{2}

  • Option 2)

    x^{2}+y^{2}=16a^{2}

  • Option 3)

    x^{2}+y^{2}=4a^{2}

  • Option 4)

    x^{2}+y^{2}=a^{2}

 

Answers (1)

As we learnt in

Equation of a circle -

x^{2}+y^{2}=r^{2}

- wherein

Circle with centre \left ( O,O \right ) and radius r.

 AD=3a

AO =2a

Centroid divides median in 2 : 1

Hence equation is 

\\ x^{2}+y^{2} =(2a)^{2} \\ x^{2}+y^{2} =4a^{2}

 


Option 1)

x^{2}+y^{2}=9a^{2}

This option is incorrect.

Option 2)

x^{2}+y^{2}=16a^{2}

This option is incorrect.

Option 3)

x^{2}+y^{2}=4a^{2}

This option is correct.

Option 4)

x^{2}+y^{2}=a^{2}

This option is incorrect.

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