C

2010006004

Level: 
C
The equation of a parabola is given by \( x^2 -8x +3y-2=0 \). Find the equation of a line, which passes through the vertex of this parabola and is parallel to the line \( 2x-5y+8=0 \).
\( -2x+5y-22 = 0 \)
\( 2x-5y-22 = 0 \)
\( 2x-5y-38 = 0 \)
\( 2x-5y+38 = 0 \)
\( -2x+5y+22 = 0 \)

2010006003

Level: 
C
Find the set of values of the parameter \( c\in\mathbb{R} \) for which the line \( 5x-3y-c=0 \) isn't a secant of the ellipse \( 25x^2+16y^2=400 \).
\( (-\infty;-25 ] \cup [ 25;\infty) \)
\( (-25;25) \)
\( \{-25,25\} \)
\( (-\infty;-25) \cup (25;\infty) \)
\( [ 25;\infty) \)

2010005904

Level: 
C
Find a true statement about the ellipse \[ 9 x^{2} + y^{2} + 18x = 0. \]
The tangent to the ellipse can pass through any point on the line \(x = 1\).
The tangent to the ellipse can pass through any point on the line \(y = 1\).
The tangent to the ellipse can pass through the point \([-1;1]\).
The tangent to the ellipse can pass through any point on the line \(y = -1\).