Find the equation of the parabola with vertex | vedclass

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Question

(A) The vertex of the parabola is $V(0, 1)$ and the focus is $F(0, 0)$.Since the $x$-coordinates are the same,the axis of the parabola is the $y$-axis

Vedclass · Accepted Answer

$x^2 + 4y - 4 = 0$

Vedclass · Answer

(A) The vertex of the parabola is $V(0, 1)$ and the focus is $F(0, 0)$.Since the $x$-coordinates are the same,the axis of the parabola is the $y$-axis $(x = 0)$.The parabola opens downwards because the focus is below the vertex.The distance $a$ between the vertex and the focus is $|1 - 0| = 1$.The standard equation of a downward-opening parabola with vertex $(h, k)$ is $(x - h)^2 = -4a(y - k)$.Substituting $h = 0, k = 1$,and $a = 1$:$(x - 0)^2 = -4(1)(y - 1)$$x^2 = -4y + 4$$x^2 + 4y - 4 = 0$.

Find the equation of the parabola with vertex at $(0, 1)$ and focus at $(0, 0)$.

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