Through a fixed point (h,k) secants are drawn to the circle x^{2 }+ y^{2}=a^{2}. The locus of the mid points of the secants intercepted by the given circle is ....??

My Answer: x^{2 }+ y^{2}= 2(hx + ky)

Book's Answer : x^{2 }+ y^{2}= (hx + ky)

Here's what i did:

Maybe the book is correct but i can't figure out what wrong I did.