Conics

1103040104

Level: 
B
The picture shows a hyperbola drawn in the rectangular coordinate system. What is the eccentricity of this hyperbola?
The distance of points \( S \) and \( F \)
The distance of points \( S \) and \( A \)
The distance of points \( A \) and \( B \)
The distance of points \( E \) and \( F \)

1103040102

Level: 
A
The diagram of an ellipse in the rectangular coordinate system is shown in the picture. Find the standard form equation of this ellipse:
\( \frac{(x-3)^2}4+\frac{(y-3)^2}9=1 \)
\( \frac{(x-3)^2}9+\frac{(y-3)^2}4=1 \)
\( \frac{(x+3)^2}4+\frac{(y+3)^2}9=1 \)
\( \frac{(x+3)^2}9+\frac{(y+3)^2}4=1 \)

1003024111

Level: 
C
The equation of a parabola is given by \( y^2 -12x -6y+57=0 \). Find the equation of a line, which passes through the vertex of this parabola and is parallel to the line \( 5x-3y-2=0 \).
\( 5x-3y-11 = 0 \)
\( -5x+3y-11 = 0 \)
\( 5x-3y-3 = 0 \)
\( 5x-3y+11 = 0 \)
\(-5x+3y-3 = 0 \)