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Equation of the circle with centre on th...

Equation of the circle with centre on the `y`-axis and passing through the origin and `(2, 3)` is

A

`x^(2)+y^(2)+13y=0`

B

`3x^(2)+3y^(2)+13x+3=0`

C

`6x^(2)+6y^(2)-13y=0`

D

`x^(2)+y^(2)+13x+3=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Let general equation of the circle is `x^(2)+y^(2)+2gh+2fy+c=0`

Since the point `(0,0)` and `(2,3)` lie on it `c=0`
`therefore` `4+9+4g+6f=0`
`rArr2g+3f=-13/2`
Since the centre lie on `Y`-axis, then `g=0`
`therefore 3f=-13/2`
`rArr f=-13/6`
So, the equation of the circle is
`x^(2)+y^(2)-(13y)/6=0`
`rArr6x^(2)+6y^(2)-13y=0`
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