Find the coordinates of the focus axis of the parabola, the equation of directrix and the length of the latus rectum for the parabola x2=−16y.
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The given equation is x2=−16y Here, the coefficient of y is negative. Hence the parabola opens downwards. On comparing this equation with x2=−4ay −4a=−16 ⇒a=4 ∴ Coordinates of the focus =(0,−a)=(0,−4) Axis of the parabola is the y-axis i.e x=0 Equation of directrix y=a i.e., y=4 Length of latus rectum =4a=16