The equation of the latus rectum of the parab | vedclass

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(C) Given the equation: ${y^2} + 2By + 2Ax + C = 0$Completing the square for $y$: $(y + B)^2 - B^2 + 2Ax + C = 0$$(y + B)^2 = -2Ax + B^2 - C$$(y + B)^

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$x = \frac{{{B^2} - {A^2} - C}}{{2A}}$

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(C) Given the equation: ${y^2} + 2By + 2Ax + C = 0$Completing the square for $y$: $(y + B)^2 - B^2 + 2Ax + C = 0$$(y + B)^2 = -2Ax + B^2 - C$$(y + B)^2 = -2A(x - \frac{B^2 - C}{2A})$This is in the form $(y - k)^2 = -4a(x - h)$,where $4a = 2A$,so $a = \frac{A}{2}$.The vertex is $(h, k) = (\frac{B^2 - C}{2A}, -B)$.The focus of a parabola $(y - k)^2 = -4a(x - h)$ is $(h - a, k)$.Focus $= (\frac{B^2 - C}{2A} - \frac{A}{2}, -B) = (\frac{B^2 - C - A^2}{2A}, -B)$.The equation of the latus rectum is $x = h - a$.$x = \frac{B^2 - C}{2A} - \frac{A}{2} = \frac{B^2 - C - A^2}{2A}$.

The equation of the latus rectum of the parabola represented by the equation ${y^2} + 2Ax + 2By + C = 0$ is

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