Points (6, −2) and (a, 6) are on a line with a slope of 4/3. What is the value of a?
A−2
B4.5
C9
D12
Mathematics · Question Bank
Analytic Geometry
233 questions · page 11 of 12. Answer in your head first, then check the solution.
If the line \(kx + 3y + 8 = 0\) has a slope of 2/3, determine k.
A−3
B−2
C3
D2
What is the length of the latus rectum of the parabola \(x^2 = -16y\)?
A4
B8
C16
D32
What is the equation of the normal to the curve \(x^2 + y^2 = 25\) at (4, 3)?
A4x + 3y = 25
B3x − 4y = 0
C4x − 3y = 7
D3x + 4y = 24
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
The eccentricity of the hyperbola having the rectangular equation \(3x^2 - 4y^2 - 24x + 16y + 20 = 0\) is
A1.12
B1.22
C1.32
D1.42
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)
An equilateral triangle is inscribed in the parabola \(x^2 = 8y\) such that one of its vertices is at the origin. Find the length of the side of the triangle.
A22.51
B24.25
C25.98
D27.71
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
The cross-section of a trough is a semi-ellipse with a width at the top of 18 cm and a depth of 12 cm. The trough is filled with water to a depth of 8 cm. Find the width at the surface of the water.
A\(5\sqrt{2}\) cm
B\(12\sqrt{2}\) cm
C\(7\sqrt{2}\) cm
D\(6\sqrt{2}\) cm