What is the point of intersection of the latu | vedclass

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(D) The point of intersection of the latus rectum and the axis of a parabola is its focus.Given the equation of the parabola: $y^2 - 4y - 2x - 8 = 0$.

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(D) The point of intersection of the latus rectum and the axis of a parabola is its focus.Given the equation of the parabola: $y^2 - 4y - 2x - 8 = 0$.Rewrite the equation by completing the square for $y$:$(y^2 - 4y + 4) - 4 - 2x - 8 = 0$$(y - 2)^2 = 2x + 12$$(y - 2)^2 = 2(x + 6)$Comparing this with the standard form $(y - k)^2 = 4a(x - h)$,we get:$h = -6$,$k = 2$,and $4a = 2 \implies a = 1/2$.The focus of the parabola is given by $(h + a, k)$.Focus $= (-6 + 1/2, 2) = (-11/2, 2)$.

What is the point of intersection of the latus rectum and the axis of the parabola $y^2 - 4y - 2x - 8 = 0$?

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