Project ID:
6000000070
Accepted:
Typ:
Layout:
Question:
Priraďte každému stredovému tvaru rovnice hyperboly jej obrázok v kartézskej sústave súradníc.
Questions Title:
Obrázky:
Answers Title:
Rovnica:
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);
}}