Question

Consider the parabola $y^2+2x+2y-3=0$ and match the items of list- I with those of the List- II

List - I		List -II
A	$2x-5=0$	I	Vertex
B	$\left(\frac{3}{2},-1\right)$	II	Focus
C	$y+1=0$	III	Equation of directrix
D	$(2,-1)$	IV	Equation of the axis
		V	Equation of Latus rectum

• A. A - (III) , B - (II) , C - (IV) ,D - (I)
• B. A - (V) , B - (I) , C - (IV) ,D - (II)
• C. A - (III) , B - (II) , C - (V) ,D - (I)
• D. A - (IV) , B - (I) , C - (III) ,D - (II)

Answer 1

Answer: (A)

We have, equation of parabola is
$y^2+2x+2y-3=0$
$\Rightarrow (y+1{)}^2-1+2x-3=0$
$\Rightarrow (y+1{)}^2=4-2x$
$\Rightarrow (y+1{)}^2=-2(x-2)$
$\therefore$ Vertex $=(2,-1)$
Axis : $y+1=0$
Focus : $(-a+2,-1)=\left(-\frac{1}{2}+2,-1\right)$
$=\left(\frac{3}{2},-1\right)$
Directrix : $x-2=\frac{1}{2}$
$\Rightarrow x=\frac{5}{2}$
$\Rightarrow 2x-5=0$