Question

The extremities of latus rectum of a parabola are $(1,1)$ and $(1,-1)$. Then the equation(s) of the parabola is/are

• A. $y^2=2x-1$
• B. $y^2=1-2x$
• C. $y^2=3-2x$
• D. $y^2=2x-3$

Answer 1

Answer: (A), (C)

The correct options are
A $y^2=2x-1$
C $y^2=3-2x$

Given that the extremities of the latus rectum are $(1,1)$ and $(1,-1)$. Then,
$4a=2$ or $a=\frac{1}{2}$
So, the focus of the parabola is $(1,0)$
Hence, the vertex can be $(\frac{1}{2},0)$ or $(\frac{3}{2},0)$
Therefore, for the vertex $(\frac{1}{2},0)$, the equations of the parabola can be $y^2=2(x-\frac{1}{2})$

For the vertex $(\frac{3}{2},0)$, the equation of parabola $y^2=-2(x-\frac{3}{2})$

i.e. $y^2=2x-1$
or $y^2=3-2x$