Hyperbola and Its Equation I

Project ID: 
6000000070
Accepted: 
SubArea: 
Type: 
Layout: 
Question: 
Match each given standard form equation of a hyperbola with its diagram.
Questions Title: 
Graphs:
Answers Title: 
Equations:
Question 1: 
{\obrA}
Question 1 Image: 
Answer 1: 

$\frac{(x-1)^2}4-y^2=1$

Question 2: 
{\obrB}
Question 2 Image: 
Answer 2: 

$(x-1)^2-\frac{y^2}4=1$

Question 3: 
{\obrC}
Question 3 Image: 
Answer 3: 

$x^2-\frac{(y-1)^2}4=1$

Question 4: 
{\obrD}
Question 4 Image: 
Answer 4: 

$\frac{x^2}4-(y-1)^2=1$

Tex: 
% tiket 32388 \NastavOD{4} \NastavOT[0pt]{4} \def\obrA{\obrMsr[x=0.25cm,y=0.5cm]{-4}{6}{-3}4 { \footnotesize \obrClip \obrOsaX[above left, xshift=2pt] \obrOsaY[below right] \obrPopisX[below]{-3,5} \obrPopisX[below]{3} \obrPopisX[below]{-1} \obrPopisY[above right, xshift=-1pt]{1} \obrZnackyY{1.73205} \obrZnackyX{1} \draw[thin,dashed] (-3,0) -- (-3,1.73205) -- (5,1.73205) -- (5,0); \draw[thin,dashed] (-1,0) -- (-1,1) -- (3,1) -- (3,0); \obrFce[black,thin]{1/2*((\x)-1)} \obrFce[black,thin]{-1/2*((\x)-1)} \obrFce[domain=-4:-1]{(((\x)-1)^2/4-1)^(1/2)} \obrFce[domain=-4:-1]{-(((\x)-1)^2/4-1)^(1/2)} \obrFce[domain=3:6]{(((\x)-1)^2/4-1)^(1/2)} \obrFce[domain=3:6]{-(((\x)-1)^2/4-1)^(1/2)} \draw (1,0) node [below,yshift=-2pt]{$S$}; \draw (0,1.73205) node [above right, xshift=-1pt]{$\sqrt3$}; \fill[blue] (-3,1.73205) circle (2pt); \fill[blue] (5,1.73205) circle (2pt); \fill[blue] (-1,1) circle (2pt); \fill[blue] (3,1) circle (2pt); }} \def\obrB{\obrMsr[x=0.4cm,y=0.4cm]{-1.5}{3.5}{-4}6 { \footnotesize \obrClip \obrOsaX[above left,xshift=4pt] \obrOsaY[below right] \obrPopisX[below]{-1,2,3} \obrPopisY[above right]{2} \obrZnackyY{2*1.73205} \obrZnackyX{1} \draw[thin,dashed] (-1,0) -- (-1,2*1.73205) -- (3,2*1.73205) -- (3,0); \draw[thin,dashed] (0,2) -- (2,2) -- (2,0); \obrFce[black,thin]{2*((\x)-1)} \obrFce[black,thin]{-2*((\x)-1)} \obrFce[domain=-2:0]{2*(((\x)-1)^2-1)^(1/2)} \obrFce[domain=-2:0]{-2*(((\x)-1)^2-1)^(1/2)} \obrFce[domain=2:5]{2*(((\x)-1)^2-1)^(1/2)} \obrFce[domain=2:5]{-2*(((\x)-1)^2-1)^(1/2)} \draw (1,0) node [below,yshift=-2pt]{$S$}; \draw (0,2*1.73205) node [above right, xshift=2pt]{$2\sqrt3$}; \fill[blue] (-1,2*1.73205) circle (2pt); \fill[blue] (3,2*1.73205) circle (2pt); \fill[blue] (2,2) circle (2pt); }} \def\obrC{\obrMsr[x=0.6cm,y=0.4cm]{-2.5}{2.5}{-3}7 { \footnotesize \obrClip \obrOsaX[above left, xshift=4pt] \obrOsaY[below right] \obrPopisX[below]{-2,2} \obrPopisX[below right]{-1} \obrPopisX[below left]{1} \obrZnackyY{1,2*1.73205+1,3,-1} \draw[thin,dashed] (-2,0) -- (-2,2*1.73205+1) -- (2,2*1.73205+1) -- (2,0); \draw[thin,dashed] (-1,-1) -- (-1,3) -- (1,3) -- (1,-1) -- cycle; \draw[thin,dashed] (-3,1) -- (4,1); \obrFce[black,thin]{2*((\x))+1} \obrFce[black,thin]{-2*((\x))+1} \obrFce[domain=-3:-1]{2*((\x)^2-1)^(1/2)+1} \obrFce[domain=-3:-1]{-2*((\x)^2-1)^(1/2)+1} \obrFce[domain=1:5]{2*((\x)^2-1)^(1/2)+1} \obrFce[domain=1:5]{-2*((\x)^2-1)^(1/2)+1} \draw (0,1) node [left,xshift=-2pt]{$S$}; \draw (0,2*1.73205+1) node [above right,xshift=-2pt]{$2\sqrt3+1$}; \draw (0,3) node [above right,xshift=-2pt]{$3$}; \draw (0,-1) node [below right,xshift=-2pt]{$-1$}; \fill[blue] (-2,2*1.73205+1) circle (2pt); \fill[blue] (2,2*1.73205+1) circle (2pt); \fill[blue] (-1,1) circle (2pt); \fill[blue] (1,1) circle (2pt); \fill[blue] (-1,3) circle (2pt); \fill[blue] (1,3) circle (2pt); \fill[blue] (-1,-1) circle (2pt); \fill[blue] (1,-1) circle (2pt); }} \def\obrD{\obrMsr[x=0.25cm,y=0.5cm]{-5.5}{5.5}{-2}5 { \footnotesize \obrClip \obrOsaX[above left] \obrOsaY[below right] \obrPopisX[below left, xshift=2pt]{-4} \obrPopisX[below]{-2,2} \obrPopisX[below right,xshift=-2pt]{4} \obrZnackyY{1,1.73205+1} \draw[thin,dashed] (-4,0) -- (-4,1.73205+1) -- (4,1.73205+1) -- (4,0); \draw[thin,dashed] (-2,0) -- (-2,2) -- (2,2) -- (2,0); \draw[thin,dashed] (-6,1) -- (6,1); \obrFce[black,thin]{1/2*((\x))+1} \obrFce[black,thin]{-1/2*((\x))+1} \obrFce[domain=-6:-2]{((\x)^2/4-1)^(1/2)+1} \obrFce[domain=-6:-2]{-((\x)^2/4-1)^(1/2)+1} \obrFce[domain=2:6]{((\x)^2/4-1)^(1/2)+1} \obrFce[domain=2:6]{-((\x)^2/4-1)^(1/2)+1} \draw (0,1) node [below left,xshift=3pt,yshift=-1pt]{$S$}; \draw (0,2) node [above right,xshift=-2pt,yshift=-1pt]{$2$}; \draw (0,1.73205+1) node [above right, xshift=-2pt]{$\sqrt3+1$}; \fill[blue] (-4,1.73205+1) circle (2pt); \fill[blue] (4,1.73205+1) circle (2pt); \fill[blue] (-2,1) circle (2pt); \fill[blue] (2,1) circle (2pt); \fill[blue] (-2,2) circle (2pt); \fill[blue] (2,2) circle (2pt); }}