Question

find the cordinates of focus ,axis of parabola, equation of directrix, and length of latus rectum of the equation y=12x​

Answer 1

The given equation is y2 = 12x. Here, the coefficient of x is positive. Hence, the parabola opens towards the right. On comparing this equation with y2 = 4ax, we obtain 4a = 12 ⇒ a = 3 ∴ Coordinates of the focus = (a, 0) = (3, 0) Since the given equation involves y2, the axis of the parabola is the x-axis. Equation of direcctrix, x = –a i.e., x = – 3 i.e., x + 3 = 0 Length of latus rectum = 4a = 4 × 3 = 12

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