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  • The vertex of a parabola is the point (a, b) and latus−rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equati

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

 

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

best_answer

The equation of the parabola referred to its vertex as the origin is \mathrm{X^2=l Y} where \mathrm{x = X + a, y = Y + b.}

Therefore the equation of the parabola referred to the point (a, b) as the vertex is \mathrm{(x-a)^2=l(y-b).} or  \mathrm{(x-a)^2=\frac{l}{2}(2 y-2 b)}

Hence answer is (b).

 

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