A parabola having its axis parallel to the Y- | vedclass

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(D) The equation of a parabola with its axis parallel to the $Y$-axis is given by $(x - h)^2 = 4a(y - k)$.Substituting the given points $(0, 2/5)$,$(4

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$(2, 8/5)$

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(D) The equation of a parabola with its axis parallel to the $Y$-axis is given by $(x - h)^2 = 4a(y - k)$.Substituting the given points $(0, 2/5)$,$(4, -2)$,and $(1, 8/5)$ into the equation:$(0 - h)^2 = 4a(2/5 - k) \implies h^2 = 4a(2/5 - k) \quad (i)$$(4 - h)^2 = 4a(-2 - k) \quad (ii)$$(1 - h)^2 = 4a(8/5 - k) \quad (iii)$Subtracting $(iii)$ from $(i)$: $h^2 - (1 - h)^2 = 4a(2/5 - 8/5) \implies 2h - 1 = -24a/5 \implies a = -5(2h - 1)/24$.Solving the system of equations,we find $h = 3/2$,$k = 7/4$,and $a = -5/12$.The equation of the parabola is $(x - 3/2)^2 = -5/3(y - 7/4)$.Checking the point $(2, 8/5)$:$(2 - 3/2)^2 = (1/2)^2 = 1/4$.$-5/3(8/5 - 7/4) = -5/3(32/20 - 35/20) = -5/3(-3/20) = 1/4$.Since $1/4 = 1/4$,the point $(2, 8/5)$ lies on the parabola.

$A$ parabola having its axis parallel to the $Y$-axis passes through the points $(0, 2/5)$,$(4, -2)$,and $(1, 8/5)$. Which of the following points lies on this parabola?

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