Discussion Forum



1)

 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

Answer:

Option B

Explanation:

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

     $x+2= -\frac{1}{2}$

$\Rightarrow$   $x+\frac{5}{2}=0$

$\Rightarrow$    $2x+5=0$