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Q.
The extremities of latus rectum of a parabola are $(1,1)$ and $(1,-1)$. Then the equation of the parabola can be
Conic Sections
Solution:
Given that the extremities of the latus rectum are $(1,1)$ and $(1,-1)$. Then,
$4 a=2$ or $a=\frac{1}{2}$
Also, the focus of the parabola is $(1,0)$.
Hence, the vertex can be $(1 / 2,0)$ or $(3 / 2,0)$.
Therefore, the equations of the parabola can be
$y^2=2\left(x-\frac{1}{2}\right)$
or $ y^2=-2\left(x-\frac{3}{2}\right)$
i.e., $ y^2=2 x-1$
or $ y^2=3-2 x$