Q96 / 160 · AP EAMCET 2007 · Mathematics

For the parabola $y^2+6 y-2 x+5=0$ (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 true
  • Correct answer
    B
    I is true, II is false
  • C
    I is false, II is true
  • D
    Both I and II are false

Solution

Given parabola is $y^2+6 y-2 x+5=0$ $\begin{array}{rlrl}\Rightarrow & y^2+6 y+9-9-2 x+5 & =0 \\ \Rightarrow & & (y+3)^2= & 2 x+4 \\ \Rightarrow & & (y+3)^2=2(x+2)\end{array}$ Vertex of parabola is $(-2,-3)=(h, k)$ Equation of directrix is $x-h+a=0$ $\begin{array}{r}x+2+\frac{1}{2}=0 \\ 2 x+5=0\end{array}$ $\therefore \mathrm{I}$ is true and $\mathrm{II}$ is false.

Hence, the correct answer is option: 'B'.

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