Project ID:
6000000067
Accepted:
Typ:
Layout:
Question:
Dopasuj wykres krzywej stożkowej do równania.
Questions Title:
Wykresy:
Answers Title:
Równania:
Question 1:
{\obrA}
Question 1 Image:
Answer 1:
$(x+1)^2+y^2=9$
Question 2:
{\obrB}
Question 2 Image:
Answer 2:
$\frac{(x+1)^2}9+y^2=1$
Question 3:
{\obrC}
Question 3 Image:
Answer 3:
$(x+1)^2-\frac{y^2}9=1$
Question 4:
{\obrD}
Question 4 Image:
Answer 4:
$(y-1)^2=4x$
Answer 5:
$(x-1)^2-\frac{y^2}9=1$
Answer 6:
$\frac{(x-1)^2}9+y^2=1$
Tex:
% tiket 32389
\NastavOD{3}
\def\obrA{\obrMsr[x=0.4cm,y=0.4cm]{-6}{4}{-5}5
{
\footnotesize
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below left]{-4}
\obrPopisX[below right]{2}
\obrZnackyX{-1}
\draw[red,thick] (-1,0) node [below,yshift=-1pt]{\color{black}$S$} circle (3);
}}
\def\obrB{\obrMsr[x=0.5cm,y=0.5cm]{-6}{4}{-4}4
{
\footnotesize
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below left]{-4}
\obrPopisX[below right]{2}
\obrPopisY[above right]{1}
\obrPopisY[below right]{-1}
\obrZnackyX{-1}
\draw[dashed] (-1,-1) -- (0,-1);
\draw[dashed] (-1,1) -- (0,1);
\draw (-1,-2) -- (-1,2);
\draw[red,thick] (-1,0) node [below left,yshift=-1pt]{\color{black}$S$} ellipse (3 and 1);
}}
\def\obrC{\obrMsr[x=0.5cm,y=0.3cm]{-6}{4}{-7}7
{
\footnotesize
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below left]{-2,-3}
\obrPopisX[below right]{0,1}
\obrPopisY[left]{3,-3}
\obrZnackyX{-1}
\obrZnackyY{-5.196152424, 5.196152424}
\draw[dashed] (1,{3*3^(1/2)}) -- (1,{-3*3^(1/2)});
\draw[dashed] (-3,{3*3^(1/2)}) -- (-3,{-3*3^(1/2)});
\draw[dashed] (-3,{-3*3^(1/2)}) -- (1,{-3*3^(1/2)});
\draw[dashed] (-3,{3*3^(1/2)}) -- (1,{3*3^(1/2)});
\obrFce[domain=-6:-2.008]{(9*((\x)+1)^2-9)^(1/2)}
\obrFce[domain=-2.01:-2]{(9*((\x)+1)^2-9)^(1/2)}
\obrFce[domain=-6:-2.008]{-(9*((\x)+1)^2-9)^(1/2)}
\obrFce[domain=-2.01:-2]{-(9*((\x)+1)^2-9)^(1/2)}
\obrFce[domain=0.008:6]{(9*((\x)+1)^2-9)^(1/2)}
\obrFce[domain=0:0.01]{(9*((\x)+1)^2-9)^(1/2)}
\obrFce[domain=0.008:6]{-(9*((\x)+1)^2-9)^(1/2)}
\obrFce[domain=0:0.01]{-(9*((\x)+1)^2-9)^(1/2)}
\obrFce[thin,dashed]{3*(\x)+3}
\obrFce[thin,dashed]{-3*(\x)-3}
\draw (0,5.196152424) node [above left]{$3\sqrt3$};
\draw (0,-5.196152424) node [below left]{$-3\sqrt3$};
\draw (-1,0) node [below,yshift=-3pt]{$S$};
}}
\def\obrD{\obrMsr[x=0.6cm,y=0.5cm]{-3}{5}{-4}5
{
\footnotesize
\coordinate (A) at (1,1);
\obrClip
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below left]{-1,0}
\obrPopisX[below right]{1}
\obrPopisY[above left]{2,1}
\obrZnackyX{0.25}
\draw[dashed] (0,2) -- (0.25,2) -- (0.25,0);
\draw[dashed] (1,0) -- (1,1);
\draw (-1,-5) -- (-1,5);
\draw (-3,1) -- (5,1);
\obrFce[domain=0:7]{(4*(\x))^(1/2)+1}
\obrFce[domain=0:7]{-(4*(\x))^(1/2)+1}
\draw (-1,4) node [above left]{$d$};
\obrKrizek[2pt] {A}{above right}{F}
\draw (0.25,0) node [below,yshift=-4pt]{$\frac14$};
}}