9000149705 Level: AFind the center of the following ellipse. \[ 16x^{2} + 9y^{2} - 32x - 54y - 47 = 0 \]\([1;3]\)\([1;-3]\)\([-1;3]\)\([-1;-3]\)
9000149706 Level: BFind the center of the following hyperbola. \[ 4x^{2} - 3y^{2} + 8x - 30y - 49 = 0 \]\([-1;-5]\)\([-1;5]\)\([1;-5]\)\([1;5]\)
9000149707 Level: BFind the center of the following hyperbola. \[ 5x^{2} - 6y^{2} - 30x + 12y + 9 = 0 \]\([3;1]\)\([3;-1]\)\([-3;1]\)\([-3;-1]\)
9000149710 Level: BFind the vertex of the following parabola. \[ x^{2} - 6x - 12y - 3 = 0 \]\([3;-1]\)\([3;1]\)\([-3;1]\)\([-3;-1]\)
9000149709 Level: BFind the vertex of the following parabola. \[ y^{2} - 12x + 4y + 64 = 0 \]\([5;-2]\)\([5;2]\)\([-5;2]\)\([-5;-2]\)
9000149708 Level: BFind the vertex of the following parabola. \[ x^{2} + 8x - 4y + 24 = 0 \]\([-4;2]\)\([-4;-2]\)\([4;2]\)\([4;-2]\)
9000149701 Level: AFind the center of the following circle. \[ x^{2} + y^{2} - 4x + 6y - 12 = 0 \]\([2;-3]\)\([-2;3]\)\([2;3]\)\([-2;-3]\)
9000149702 Level: AFind the center of the following circle. \[ x^{2} + y^{2} + 2x - 8y + 13 = 0 \]\([-1;4]\)\([-1;-4]\)\([1;4]\)\([1;-4]\)
9000149703 Level: AFind the center of the following circle. \[ x^{2} + y^{2} - 10x - 2y + 10 = 0 \]\([5;1]\)\([5;-1]\)\([-5;1]\)\([-5;-1]\)
9000123105 Level: CFind the all values of the real parameter \(p\) which ensure that the line \(q\colon y = x - 1\) is a tangent to the parabola \[ x^{2} = 2py. \]\(p = 2\)\(p\in \{0;2\}\)\(p = -2\)\(p\in \{ - 2;0\}\)