Reflection of point (h,k) in line x−y−1=0:
1x−h=−1y−k=2−2(h−k−1)=k−h+1.
Image: (k+1, h−1).
Let (X,Y)=(k+1, h−1), so h=Y+1, k=X−1.
From h2=4k: (Y+1)2=4(X−1).
Comparing with (y+a)2=b(x−c): a=1, b=4, c=1.
a+b+c=1+4+1=6.
Let the image of parabola x2=4y, in the line x−y=1 be (y+a)2=b(x−c), a,b,c∈ N. Then a+b+c is equal to
Held on 24 Jan 2026 · Verified 6 Jul 2026.
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