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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

`3x^(2)+3y^(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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