Question

The coordinates of end point of the latus rectum of the parabola $(y-1{)}^2=4(x+1)$ are

• A. $(0,-3)$
• B. $(0,-1)$
• C. $(0,1)$
• D. $(1,3)$

Answer 1

Answer: (B)

$(0,-1)$

Given equation of parabola $(y-1{)}^2=4(x-1)$

can be rewritten as $Y^2=4X....\left(i\right)$

where, $Y=y-1$ and $X=x+1$

$\Rightarrow y=Y+1$ and $x=X-1$

Thus, it is shifting the origin at $(-1,1)$

$\therefore$ From Eq. (i),

$Y^2=4X$

The coordinates of the endpoints of latus rectum are

$X=1,Y=2$ and $X=1,Y=-2$

Hence, the coordinates of the end points of the latusrectum are $(0,3)$ and $(0,-1)$.