UPSEE Solved Model Paper 3

2y

dy

dx

= x {- 2 (2 - x)} + (2−x)2 . 1
= (2 - x) (2 - x - 2x)
= (2 - x) (2 - 3x) (

dy

dx

)(1,1)
=

(2−1)(2−3)]

2

= −

1

2

∴ Equation of tangent at (1, 1) is y - 1 =

1

2

(x−1)
⇒ y = 1 -

x

2

+

1

2

= (

3

2

−

x

2

)
⇒ y2 =

(3−x)2

4

⇒ x(2−x)2 =

(3−x)2

4

[Since y2 = x(2−x)2]
after solving we gget x = 9/4
∴ y =

3

8

so, P is (

9

4

,

3

8

)