Question

Let $V$ be the vertex and $L$ be the latus rectum of the parabola $x^2=2y+4x-4$. Then the equation of the parabola whose vertex is at $V$, latus rectum is $L/2$ and axis is perpendicular to the axis of the given parabola

• A. $y^2=x-2$
• B. $y^2=x-4$
• C. $y^2=2-x$
• D. $y^2=4-x$

Answer 1

Answer: (A), (C)

The correct options are
A $y^2=x-2$
C $y^2=2-x$

Equation of parabola

$\Rightarrow x^2=2y+4x-4$

$x^2-4x=2y-4$

On Squaring both sides, we get.

$x^2-4x+4=2y$

${(x=2)}^2=2y$

Now,

The vertices this parabola is $(2,0)$

And

Length of latus rectum $=2$

Length of latus rectum of the

Required parabola $=1$

So,

${(y-0)}^2=1(x-1)$

$y^2=x-2\text{or}{\text{y}}^2=\text{2}\text{-}\text{x}$

Hence, this is the answer.