For the parabola y^2+6y-2x=-5,consider the fo | vedclass

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(B) Given equation: $y^2+6y-2x=-5$Completing the square for $y$:$y^2+6y+9 = 2x-5+9$$(y+3)^2 = 2x+4$$(y+3)^2 = 2(x+2)$Comparing this with the standard

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$I$ is true,$II$ is false

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(B) Given equation: $y^2+6y-2x=-5$Completing the square for $y$:$y^2+6y+9 = 2x-5+9$$(y+3)^2 = 2x+4$$(y+3)^2 = 2(x+2)$Comparing this with the standard form $(y-k)^2 = 4a(x-h)$,we get:Vertex $(h, k) = (-2, -3)$. Thus,statement $I$ is true.Here,$4a = 2$,so $a = \frac{1}{2}$.The directrix of the parabola $(y-k)^2 = 4a(x-h)$ is given by $x = h-a$.$x = -2 - \frac{1}{2} = -\frac{5}{2}$$2x = -5 \Rightarrow 2x+5 = 0$.Statement $II$ says the directrix is $y+3=0$,which is false.Therefore,$I$ is true and $II$ is false.

For the parabola $y^2+6y-2x=-5$,consider the following statements:
$I$. The vertex is $(-2, -3)$.
$II$. The directrix is $y+3=0$.
Which of the following is correct?

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For the parabola $y^2+6y-2x=-5$,consider the following statements:$I$. The vertex is $(-2, -3)$.$II$. The directrix is $y+3=0$.Which of the following is correct?