Mathematics | TS EAMCET 2017 | Discussion Page

For the parabola $y^{2}+6y-2x=-5$

I. the vertex is (-2,-3)

II. the directrix is y+3=0

Which of the following is correct?

A) Both I and II are correct

B) I is true , II is false

C) Both I and II are false

D) I is false, II is true

Option B

We have,

$y^{2}+6y-2x=-5$

$\Rightarrow$ $y^{2}+6y=2x-5$

$\Rightarrow$ $y^{2}+6y+9=2x-5+9$

$\Rightarrow$ $(y+3)^{2}=2x+4$

$\Rightarrow$ $(y+3)^{2}=2(x+2)$

$\therefore$ 4a=2 $\Rightarrow$ a= $\frac{1}{2}$

Vertex=(-2,-3)

Equations of directrix

$x+2= -\frac{1}{2}$

$\Rightarrow$ $x+\frac{5}{2}=0$

$\Rightarrow$ $2x+5=0$

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