The equation of the parabola whose vertex is | vedclass

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(B) The vertex $V$ is $(h, k) = (2, -1)$ and the focus $S$ is $(2, -3)$.Since the $x$-coordinates of the vertex and focus are the same,the axis of the

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${x^2} - 4x + 8y + 12 = 0$

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(B) The vertex $V$ is $(h, k) = (2, -1)$ and the focus $S$ is $(2, -3)$.Since the $x$-coordinates of the vertex and focus are the same,the axis of the parabola is vertical.The distance $a$ between the vertex and the focus is $a = | -1 - (-3) | = 2$.Since the focus is below the vertex,the parabola opens downwards.The standard equation for a downward-opening parabola is $(x - h)^2 = -4a(y - k)$.Substituting the values $h = 2$,$k = -1$,and $a = 2$:$(x - 2)^2 = -4(2)(y - (-1))$$(x - 2)^2 = -8(y + 1)$Expanding the equation:$x^2 - 4x + 4 = -8y - 8$$x^2 - 4x + 8y + 12 = 0$.Thus,the correct option is $B$.

The equation of the parabola whose vertex is at $(2, -1)$ and focus at $(2, -3)$ is

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