What conic section is 2x² - 8xy + 4x = 12?
AParabola
BEllipse
CHyperbola
DCircle
Mathematics · Question Bank
Analytic Geometry
44 of 233 questions match · page 1 of 3. Answer in your head first, then check the solution.
What conic section is described by the equation r = 6 / (4 – 3cosӨ)?
ACircle
BEllipse
CHyperbola
DParabola
If the second-degree equation Ax² + Bxy + Cy² +Dx + Ey + F = 0 represents a real conic and B² – 4AC is positive, then it is
Aellipse
Bcircle
Cparabola
Dhyperbola
If the slopes of two lines are equal and their y-intercepts are different, then the lines are
Aintersecting
Bparallel
Ccoincident
Dperpendicular
A line with inclination between 0° and 90° has
Azero slope
Bno slope
Cpositive slope
Dnegative slope
The parabola x² – 4x + 2y – 6 = 0 opens
Adownward
Bupward
Cto the right
Dto the left
The locus of a point on a circle which rolls without slipping on a straight line is called
Astrophoid
Btrochoid
Castroid
Dcycloid
If b² – 4ac < 0, then the graph of y = ax² + bx + c
Acrosses the x-axis once
Bcrosses the x-axis twice
Cdoes not cross the x-axis
Dtouches the x-axis once
The slope of a vertical line is
Azero
Bone
C90°
Dundefined
If the inclination θ of a line is an obtuse angle, then the tangent of θ is
Apositive
Bnegative
Czero
Dinfinity
The ellipse is symmetric with respect to
Athe x-axis only
Bthe y-axis only
Cthe origin only
Dboth axes and the origin
If a line slants downward to the right, then it has
Anegative slope
Bpositive slope
Cno slope
Dzero slope
If the directed distance from a point to the line is negative, then which of the following is true?
AThe point and the origin are not on the side of the line.
BThe point and the origin are on the opposite sides of the line.
CThe point is below the line.
DThe point is above the line.
Which of the following is the polar equation of a limacon?
Ar = 1 + sinθ
Br = 2(1 – sinθ)
Cr = 2 – sinθ
Dr = 2sinθ
If the eccentricity of a conic is greater than one, then it is a
Aan ellipse
Ba circle
Ca parabola
Da hyperbola
The graph of 3x² – y = y² + 6x is
Aa parabola
Ban ellipse
Ca circle
Da hyperbola
If the value of the invariant B² – 4AC is negative, then the second-degree equation Ax² + Bxy +Cy² + Dx + Ey + F = 0 represents either an ellipse or
Aa pair of parallel lines
Btwo intersecting lines
Ca point
Da line
The surface described by the equation 4x² + y² + 26z = 100 is an
Aelliptic hyperboloid
Belliptic paraboloid
Cellipsoid
Delliptic cone
The locus of 9x² – 4z² – 36y = 0 is a/an
Aelliptic cone
Bhyperbolic paraboloid
Cparabolic cylinder
Dellipsoid
The trace of x² + 4z² – 8y = 0 on the xy-plane is
Aa hyperbola
Ban ellipse
Ca parabola
Da point