Consider the parabola y2+2x+2y−3=0 and match the items of List – I with those of the List-II List – I List – IIA)2x−5=0I)VertexB)32,−1II)FocusC)y+1=0III)Equation of directrixD)(2, −1)IV)Equation of axis V)Equation of latus rectum

y2+2x+2y−3=0⇒y2+2y=−2x+3⇒y2+2y+1=−2x+4⇒y+12=−2x−2→ 1(1) Is in the form ofy−k2=−4ax−h⇒4a=2⇒a=12 Where vertex A=h,k=2,−1 Focus S=h−a,k=2−12,−1=32,−1Directrix x−h=a x−2=12⇒2x−5=0 Equation of axis y+1=0

Consider the parabola y2+2x+2y−3=0 and match the items of List – I with those of the List-II List – I List – IIA)2x−5=0I)VertexB)32,−1II)FocusC)y+1=0III)Equation of directrixD)(2, −1)IV)Equation of axis V)Equation of latus rectum

y2+2x+2y−3=0⇒y2+2y=−2x+3⇒y2+2y+1=−2x+4⇒y+12=−2x−2→ 1(1) Is in the form ofy−k2=−4ax−h⇒4a=2⇒a=12 Where vertex A=h,k=2,−1 Focus S=h−a,k=2−12,−1=32,−1Directrix x−h=a x−2=12⇒2x−5=0 Equation of axis y+1=0

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Consider the parabola $y^{2} + 2 x + 2 y - 3 = 0$ and match the items of List – I with those of the List-II
List – I List – II
A) $2 x - 5 = 0$ I) Vertex
B) $(\frac{3}{2}, - 1)$ II) Focus
C) $y + 1 = 0$ III) Equation of directrix
D) $(2, - 1)$ IV) Equation of axis
V) Equation of latus rectum

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A – III, B – II, C – IV, D – I

A – V, B – I, C – IV, D – II

A – III, B – II, C – V, D – I

A – IV, B – I, C – III, D – II

answer is A.

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Detailed Solution

$y^{2} + 2 x + 2 y - 3 = 0$

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

$\Rightarrow y^{2} + 2 y + 1 = - 2 x + 4$

$\Rightarrow {(y + 1)}^{2} = - 2 (x - 2) \overset{}{\to} (1)$

(1) Is in the form of
${(y - k)}^{2} = - 4 a (x - h) \Rightarrow 4 a = 2 \Rightarrow a = \frac{1}{2}$
Where vertex $A = (h, k) = (2, - 1)$
Focus $S = (h - a, k) = (2 - \frac{1}{2}, - 1) = (\frac{3}{2}, - 1)$
Directrix $x - h = a$
$x - 2 = \frac{1}{2} \Rightarrow 2 x - 5 = 0$
Equation of axis
$y + 1 = 0$

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

Consider the parabola y2+2x+2y−3=0 and match the items of List – I with those of the List-II List – I List – IIA)2x−5=0I)VertexB)32,−1II)FocusC)y+1=0III)Equation of directrixD)(2, −1)IV)Equation of axis V)Equation of latus rectum

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Consider the parabola $y^{2} + 2 x + 2 y - 3 = 0$ and match the items of List – I with those of the List-II
List – I List – II
A) $2 x - 5 = 0$ I) Vertex
B) $(\frac{3}{2}, - 1)$ II) Focus
C) $y + 1 = 0$ III) Equation of directrix
D) $(2, - 1)$ IV) Equation of axis
V) Equation of latus rectum