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

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

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

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$(x + a)^{2} = \frac{l}{4} (2 y - 2 b)$

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$(x - a)^{2} = \frac{l}{8} (2 y - 2 b)$

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Solution

The correct option is B
$(x - a)^{2} = \frac{l}{2} (2 y - 2 b)$

The equation of the parabola referred to its vertex as the origin is $X^{2} = I Y$ where x = X+a, y = Y+b. Therefore the equation of the parabola referred to the point (a,b) as the vertex is $(x - a)^{2} = l (y - b) o r (x - a)^{2} = \frac{l}{2} (2 y - 2 b)$

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

The correct option is B (x−a)2=l2(2y−2b) The equation of the parabola referred to its vertex as the origin is X2=IY where x = X+a, y = Y+b. Therefore the equation of the parabola referred to the point (a,b) as the vertex is (x−a)2=l(y−b) or (x−a)2=l2(2y−2b)