Parabola
Reflection of Parabola in Line — a+b+c
nta_pyq_2026_jan
Grade 11
Question:
Let the image of parabola $x^2=4y$, in the line $x-y=1$ be $(y+a)^2=b(x-c)$, $a,b,c\in\mathbb{N}$. Then $a+b+c$ is equal to
Step-by-Step Solution
Key Concept: Reflect point $(h,k)$ in line $x-y-1=0$: image is $(k+1,h-1)$. Let image point be $(X,Y)=(k+1,h-1)$, so $h=Y+1$, $k=X-1$. From $h^2=4k$: $(Y+1)^2=4(X-1)$.
$a=1$, $b=4$, $c=1$. $a+b+c=6$.
Correct Answer: 2