The vertex of a parabola is the point (a, b) | vedclass

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(B) The standard equation of a parabola with vertex at the origin $(0, 0)$ and axis along the positive $y$-axis is $X^2 = 4AY$,where the length of the

Vedclass · Accepted Answer

$(x - a)^2 = \frac{l}{2}(2y - 2b)$

Vedclass · Answer

(B) The standard equation of a parabola with vertex at the origin $(0, 0)$ and axis along the positive $y$-axis is $X^2 = 4AY$,where the length of the latus rectum $l = 4A$,so $A = \frac{l}{4}$.Substituting $A$,we get $X^2 = lY$.Given the vertex is at $(a, b)$,we use the transformation $X = x - a$ and $Y = y - b$.Substituting these into the equation,we get $(x - a)^2 = l(y - b)$.To match the given options,we can rewrite the right side as $(x - a)^2 = \frac{l}{2}(2y - 2b)$.

The vertex of a parabola is the point $(a, b)$ and the latus rectum is of length $l$. If the axis of the parabola is along the positive direction of the $y$-axis,then its equation is

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