Question

For the parabola $y^2 + 6\,y - 2x = - 5$ 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 1

Answer: (B)

I is true, II is false

Answer 2

We have,
$y^{2}+6 \,y-2\, x=-5$
$\Rightarrow y^{2}+6\, y=2\, x-5$
$\Rightarrow y^{2}+6\, y+9=2 x-5+9$
$\Rightarrow (y+3)^{2}=2\, x+4$
$\Rightarrow (y+3)^{2}=2(x+2)$
$\therefore 4 a=2 \Rightarrow a=\frac{1}{2}$
Vertex $=(-2,-3)$
Equations of directrix
$x+2=-\frac{1}{2}$
$\Rightarrow x+\frac{5}{2}=0$
$\Rightarrow 2 \,x+5=0$