Question

The coordinates of an endpoint of the latusrectum of the parabola $(y-1{)}^2=4(x+1)$ are

• A. $(0,3)$
• B. $(1,2)$
• C. $(0,-1)$
• D. $(1,-2)$

Answer 1

Answer: (A), (C)

The correct options are
A $(0,3)$
C $(0,-1)$

Shifting the origin at $(-1,1)$, we have
$\begin{array}{c}x=X-1\\ y=Y+1\end{array}\}\cdots \left(1\right)$
Using equation $\left(1\right)$ the given parabola becomes
$Y^2=4X$
The coordinates of the end points of latusrectum are $(X,Y)\equiv (1,2),(1,-2)$
Using equation $\left(1\right)$ the coordinates of the end points of the latusrectum are $(0,3)$ and $(0,-1)$