NIMCET 2011 — Mathematics PYQ

1. Rearrange the Equation:

Move the terms not involving $y$ to the right side of the equation:

2. Complete the Square:

To make the left side a perfect square, take half of the coefficient of $y$ (which is $-8$), square it, and add it to both sides.

Half of $-8$ is $-4$, and $(-4{)}^2=16$.

Add 16 to both sides:

3. Simplify into Standard Form:

The left side becomes a perfect square, and simplify the right side:

This can be written as:

4. Identify the Vertex:

Comparing this with the standard form $(y-k{)}^2=4a(x-h)$:

• $k=4$

• $h=3$

The vertex $(h,k)$ is $(3,4)$.

Correct Option: (a)