Give the focus, directrix, and axis for the parabola.
-$$( x - 1 ) ^ { 2 } = 8 ( y - 2 )$$
A) $( 2,3 ) , y = - 1 , x = 2$
B) $( 1,0 ) , x = 4 , y = 2$
C) $( 1,4 ) , y = 0 , x = 1$
D) $( - 1,0 ) , y = - 4 , x = - 1$

Question

Quizplus · Accepted Answer

The given equation is in the form $(x - h)^2 = 4p(y - k)$, where the vertex is at $(h, k)$ and the focus is at $(h, k + p)$. Here, $h = 1$, $k = 2$, and $4p = 8$, so $p = 2$. Thus, the focus is at $(1, 2 + 2) = (1, 4)$. The directrix is $y = k - p = 2 - 2 = 0$, and the axis of symmetry is $x = h = 1$.

Give the Focus, Directrix, and Axis for the Parabola (x−1)2=8(y−2)( x - 1 ) ^ { 2 } = 8 ( y - 2 )(x−1)2=8(y−2)

Give the Focus, Directrix, and Axis for the Parabola $( x - 1 ) ^ { 2 } = 8 ( y - 2 )$