The equation of the parabola with its vertex | vedclass

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(C) Given,the vertex of the parabola $(h, k) = (1, 1)$ and the focus $(h + a, k) = (3, 1)$.Since the $y$-coordinates of the vertex and focus are the s

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$(y - 1)^2 = 8(x - 1)$

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(C) Given,the vertex of the parabola $(h, k) = (1, 1)$ and the focus $(h + a, k) = (3, 1)$.Since the $y$-coordinates of the vertex and focus are the same,the axis of the parabola is parallel to the $x$-axis.Comparing the coordinates,we have $h = 1$,$k = 1$,and $h + a = 3$.Substituting $h = 1$ into $h + a = 3$,we get $1 + a = 3$,which implies $a = 2$.The standard equation of a parabola opening to the right with vertex $(h, k)$ is $(y - k)^2 = 4a(x - h)$.Substituting the values $h = 1$,$k = 1$,and $a = 2$,we get $(y - 1)^2 = 4(2)(x - 1)$.Therefore,the equation is $(y - 1)^2 = 8(x - 1)$.

The equation of the parabola with its vertex at $(1, 1)$ and focus at $(3, 1)$ is

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