If the line \(kx + 3y + 8 = 0\) has a slope of 2/3, determine k.
A−3
B−2
C3
D2
Mathematics · Question Bank
Analytic Geometry
128 of 233 questions match · page 6 of 7. Answer in your head first, then check the solution.
What is the length of the latus rectum of the parabola \(x^2 = -16y\)?
A4
B8
C16
D32
Determine the eccentricity of the hyperbola \(xy = 8\).
A1
B1.414
C1.732
D2
Name the type of graph represented by \(x^2 - 4y^2 - 10x - 8y = 0\).
Acircle
Bellipse
Cparabola
Dhyperbola
If the graph of \(y = (x - 2)^2 - 3\) is translated 5 units up and 2 units to the right, then the equation of the graph obtained is
A\(y = (x - 4)^2 + 2\)
B\(y = x^2 + 2\)
C\(y = (x - 4)^2 - 8\)
D\(y = (x + 4)^2 + 2\)
A line with equation \(y = mx + b\) passes through (−1/3, −6) and (2, 1). Find the value of m.
A1
B3
C4
D2
Given a conic section, if \(B^2 - 4AC = 0\), it is called?
Acircle
Bparabola
Chyperbola
Dellipse
Given a conic section, if \(B^2 - 4AC \gt 0\), it is called?
Acircle
Bparabola
Chyperbola
Dellipse
A tangent to a conic is a line
Awhich is parallel to the normal
Bwhich touches the conic at only one point
Cwhich passes inside the conic
Dall of the above
Find the slope of the line through the points (−2, 5) and (7, 1).
A4/9
B−4/9
C9/4
D1/4
For what value of k will the line \(kx + 5y = 2k\) have a y-intercept of 4?
A−10
B10
C9
D−9
It represents the distance of a point from the y-axis.
Aabscissa
Bordinate
Ccoordinate
Dpolar distance
In the polar coordinate system, the polar angle is negative when
Ameasured counterclockwise
Bmeasured clockwise
Cmeasured at the terminal side of θ
Dnone of these
Find the point along the line x = y = z that is equidistant from (3, 0, 5) and (1, −1, 4).
A(1, 1, 1)
B(2, 2, 2)
C(3, 3, 3)
D(4, 4, 4)
Find the slope of the line passing through the pair of points (−2, 0) and (3, 1).
A1/3
B1/4
C1/6
D1/5
Find the equation of the line that passes through (3, −8) and is parallel to \(2x + 3y = 2\).
A2x + 3y = −18
B2x + 3y = 30
C2x + 3y = −30
D2x + 3y = 18
Find the center of the circle \(x^2 + y^2 + 16x + 20y + 155 = 0\).
A(−8, −10)
B(8, 10)
C(8, −10)
D(−8, 10)
Name the type of graph represented by \(x^2 - 4y^2 - 10x - 8y = 0\).
Acircle
Bparabola
Cellipse
Dhyperbola
Find the distance of the directrix from the center of an ellipse if its major axis is 10 and its minor axis is 8.
A8.1
B8.3
C8.5
D8.7
What is the slope of the linear equation \(3y - x = 9\)?
A1/3
B−3
C3
D9