Conic Sections

9000104805

Level: 
C
Find the slope of a line through the center of the hyperbola \[ \frac{(x - 2)^{2}} {4} -\frac{(y + 3)^{2}} {9} = 1 \] which has a unique intersection with this hyperbola.
There is no solution, the line with these properties does not exist.
\(\frac{3} {2}\)
\(-\frac{3} {2}\)
\(\frac{2} {3}\)
\(1\)
\(0\)

9000104809

Level: 
C
Among the following lines (which all pass through the point \([-1;3]\)) identify a line which is tangent to the following hyperbola. \[ (x + 2)\cdot (y - 2) = 1 \]
\(k\colon \ y = -x + 2\)
\(p\colon \ y = 3\)
\(q\colon \ x = -1\)
\(r\colon \ y = x + 4\)
None of the given answers is correct.