UPSEE Solved Model Paper 3

Equation of circle is (x−0)2+(y−k)2 = (

k

√2

)2
⇒ x2+y2−2ky+

k2

2

= 0
∴ Equation of tangent is 2x + 2yy' - 2ky' = 0
k =

x+yy′

y′

From eq (i) we get x2+y2−2y(

x+yy′

y′

) +

(x+yy′)2

2(y′)2

= 0
⇒ 2(y′)2(x2+y2) - 4yy′(x+yy′)+(x+yy′)2 = 0
∴ Order = 1, degree = 2 i.e., a = 2 , b = 1