UPSC NDA Math Model Paper 1

Here, the centre of the circle is on Y-axis. Let the centre be (0, m)
It is passing through (0, 0) and (2, 3)
∴Distance from the centre to this point will be equal
√0+(m−0)2=√(0−2)2+(m−3)2 ⇒m2=4+m2−6m+9⇒6m=13
m=13∕6
∴ Centre of the circle (0,13∕6)
Now radius ==√0+(0−

13

6

)2=

13

6

∴ Equation of circle:
(x−0)2+(y−

13

6

)2=(

13

6

)2 ⇒x2+y2−

26

6

y+

169

36

=

169

36

⇒x2+y2−

13

3

y=0
⇒3x2+3y2−13y=0
Hence, option (2) is correct.