Question

while finding the focal length required for the corrective lens for hypermetropic eye the image distance is taken as -ve. why???

Answer 1

b/c for the correction of hypermetropic eye concave len is used. and image formed by concave lens is always -ve...

Answer 2

See,

In hypermetropic eye we use convex lens for correction. And the nearpoint of eye is 25 which will  become the object distance : u = -25
 
 now suppose  the hypermetropic person cannot see objects which are kept before 30cm in front of eye. But he can see objects clearly if the object is placed beyond 30 or at 30cm. 
 
So now we need to make the image at 30 for the hypermetropic eye so that he can see any object placed before 30cm. So we use here is convex lens which is placed in front of the eye.
Now the object distance is also in front of the lens and the image distance is also in front of the lens(convex) Which is in the  left side.
So here by sign convention we can take u = -25 and v = -30.

Hope  this clears your doubt.