UPSEE 2019 Solved Paper

Let Center of Circle is C:(0,K) , Any point on it P(X,Y) and Given Radius of Circle R=4
Then Equation of circle becomes after applying distance formula
(X−0)2+(Y−K)2=16...... (i)
Now d.w.r.t X of equation (i)
2X+2(Y−K)Y=0
(Y−K)=

(−X)

(Y)

...... (ii)
From Eq. (i) and (ii) we have get,
X2+[

(−X)

(Y)

]2=16
(XY)2+X2=(4Y)2: Represents the family of circles whose center (0,K) lies
on Y-axis and Radius is 4.