9000123101 Level: CFind the values of the real parameter q which ensure that the line y=q is a tangent to the circle x2+y2+4x−8y+4=0.{0;8}{−6;2}{−8;0}{−2;6}
9000123102 Level: CFind a true statement about the ellipse x2+4y2−8y=0.The tangent to the ellipse can pass through any point on the line y=−1.The tangent to the ellipse can pass through any point on the line x=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.
9000123103 Level: CThe ellipse 5x2+9y2=45 has tangent 2x+3y=9. Find the values of the real parameter k which ensure that the line y=kx+3 is a secant for the ellipse.k∈(−∞;−23)∪(23;∞)k∈[−23;23]k∈(−23;23)k∈(−∞;−23]∪[23;∞)
9000123104 Level: CIn the following list identify a line which is a tangent to the ellipse (x−2)2+y29=1p:x=3+t,y=3; t∈Rp:x=2p:y=3xp:y=−x−2
9000123105 Level: CFind the all values of the real parameter p which ensure that the line q:y=x−1 is a tangent to the parabola x2=2py.p=2p∈{0;2}p=−2p∈{−2;0}
9000123106 Level: CFind the tangent line q to the parabola 4(y−2)=(x+1)2, so that the tangent q is parallel to the line p:4x−5y+17=0.q:20x−25y+54=0q:20x−25y−27=0q:4x−5y+27=0q:4x−5y−17=0
9000123107 Level: CIn the following list identify a line such that the line has a unique intersection with the hyperbola x2−y2=5 but the line is not the tangent to this hyperbola.p:x5+y5=1p:y=5xp:2x+y=5p:x=1y=−1+t; t∈R
9000123108 Level: CFind all the tangents to the hyperbola x2−2y2=8 such that the angle between each tangent and the x-axis is 45∘.y=x+2, y=x−2, y=−x+2, y=−x−2y=x+2, y=x−2y=x+2, y=−x+2y=x+2