Conics

9000104801

Level: 
C
Consider the hyperbola xy=−1 and a line p parallel to one of the axes but not identical with this axis. Find the true statement.
The line p has a unique intersection with the hyperbola.
The line p has two intersections with the hyperbola.
The line p does not have any intersection with the hyperbola.
We cannot draw any conclusion on the number of intersections of the line p with the hyperbola.

9000104803

Level: 
C
Consider the hyperbola x216−y24=1 and a line p parallel to one of the axes. Find the true statement.
We cannot draw any conclusion on the number of intersections of the line p with the hyperbola.
The line p has two intersections with the hyperbola.
The line p has a unique intersection with the hyperbola.
The line p does not have any intersection with the hyperbola.

9000106901

Level: 
C
A body is thrown at the initial angle α=45∘ and the initial velocity v0=10m/s. The trajectory of the body is a parabola. Find the equation of this parabola. Hint: The coordinates of the moving body as functions of time are x=v0t⋅cos⁡α,y=v0t⋅sin⁡α−12gt2. Consider the standard acceleration due to gravity g=10m/s2.
(x−5)2=−10⋅(y−2.5)
(x−5)2=10⋅(y+2.5)
x2=−10⋅(y−5)
(x−5)2=−10⋅(y+2.5)