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Determine the focus coordinates, the axis of the parabola, the equation of the directrix and the latus rectum length for y 2 = -8x
Welcome to AskIITiansGiven that, the parabola equation is y2= -8x.It is noted that the coefficient of x is negative.Therefore, the parabola opens towards the left.Now, compare the equation with y2= -4ax, we obtain-4a= -8⇒ a = 2Thus, the value of a is 2.Therefore, the coordinates of the focus = (-a, 0) = (-2, 0)Since the given equation involves y2, the axis of the parabola is the x-axis.Equation of directrix, x= a i.e., x = 2We know the formula to find the length of a latus rectumLatus rectum length= 4aNow, substitute a = 2, we getLength of latus rectum = 8Thanks
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