Analytic Geometry Flashcards
If A is at point (-2, 5) and B is at point (3, 9), what is the length of the line segment AB?
a) 5.5
b) 5.7
c) 6.4
d) 7.1
c) 6.4
Two surveyors need to find the distance across a lake. They place a reference pole at point A in the diagram. Point B is 3 meters east and 1 meter north of the reference point A. Point C is 19 meters east and 13 meters north of point A. Find the distance across the lake, from B to C.
a) 17 m
b) 18 m
c) 19 m
d) 20 m
d) 20 m
What is the slope of a line passing through (1, 2) and (4, 6)?
a) 1/2
b) 4/3
c) 2
d) 1
b) 4/3
Consider points M, N, and P with coordinates (3, -4), (1, p), and (-5, 4), respectively. If M, N and P are collinear, what is the value of p?
a) 1
b) 2
c) -1
d) -2
b) 2
What is the angle made by the line passing through (5, -1) and (2, 3) with the x-axis?
a) 53.13°
b) 46.17°
c) 91.52°
d) 66.63°
a) 53.13°
Determine the equation of the line passing through the points (-5, 3) and (4,2).
a) x - 9y +22 = 0
b) x + 9y + 22 = 0
c) x + 9y - 22 = 0
d) x - 9y - 22 = 0
c) x +9y -22 = 0
What is the equation of the line having a slope of 2 and passing through the points (-4, 3)?
a) 2x + y + 11 = 0
b) 2x - y - 11 =0
c) 2x + y -11 = 0
d) 2x - y +11 = 0
d) 2x - y + 11 = 0
Find the equation of the line with x and intercepts -1 and 7, respectively.
a) 7x + y - 7 = 0
b) 7x + y +7 = 0
c) 7x - y + 7 = 0
d) 7x - y - 7 =0
c) 7x - y +7 = 0
Find the equation of the line perpendicular to x - 4y = 3 and passing through the point (2, -5).
a) 4x + y - 3 = 0
b) 4x + y + 3 = 0
c) 4x - y + 3 = 0
d) 4x - y - 3 = 0
a) 4x + y - 3 = 0
Determine the distance from the point (5, -3) to the line 2x - 4y + 10 = 0.
a) 6.93
b) 7.16
c) 3.45
d) 4.69
b) 7.16
Find the distance between the parallel lines x - 2y + 10 = 0 and x - 2y - 2 = 0.
a) 4.5
b) 5.4
c) 4.4
d) 4.7
b) 5.4
Determine the acute angle between the lines 4x - 3y + 9 = 0 and 3x - 8y + 1 = 0.
a) 32.57°
b) 33.51°
c) 30.21°
d) 31.17°
a) 32.57°
Determine the center of the circle with equation x² + y² - 4x + 6y -23 = 0.
a) (2, -3)
b) (2, 3)
c) (-2, 3)
d (-2, -3)
a) (2, -3)
Determine the equation of the circle passing through the points (-3, 1), (0, 4), and (3, -6).
a) 13x² + 13y² + 49x - 23y - 300 = 0
b) 13x² + 13y² - 49x + 23y - 300 = 0
c) 13x² + 13y² - 49x - 23y - 300 = 0
d) 13x² + 13y² + 49x + 23y - 300 = 0
b) 13x² + 13y² - 49x + 23y - 300 = 0
Where is the vertex of the parabola x² - 4y + 8 = 0?
a) (1, 0)
b) (0, 1)
c) (0, 2)
d) (2, 0)
c) (0, 2)
An arch 18 m high has the form of parabola with a vertical axis. The length of a horizontal beam placed across the arch 8 m from the top is 64 m. Find the width of the arch at the bottom.
a) 48 m
b) 96 m
c) 32 m
d) 64 m
b) 96 m
A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and depth 1 inch. How far from the center of the mirror will the incoming light collect?
a) 3 in
b) 4 in
c) 5 in
d) 6 in
b) 4 in
Determine the length of the latus rectum of the curve 25x² + 9y² - 300x - 144y +1251 = 0.
a) 3.2
b) 3.4
c) 3.6
d) 3.8
c) 3.6
The arch of a bridge is on the shape of a semi-ellipse having a horizontal span of 90 m and a height of 30 m at its center. How high is the arch 25 m to the right or left of the center?
a) 24.94 m
b) 28.81 m
c) 27.65 m
d) 24.10 m
a) 24.94 m
Assume that the length of the major axis of Earth’s orbit is 186,000,000 miles and that the eccentricity is 0.017. Approximate, to the nearest 1000 miles,
a. the maximum distance between Earth and the sun.
a) 94,481,000 mi
b) 94,581,000 mi
c) 94,681,000 mi
d) 94,781,000 mi
b. the minimum distance between Earth and the sun.
a) 91,219,000 in
b) 91,319,000 in
c) 91,419,000 in
d) 91,519,000 in
b) 94,581,000
c) 91,419,000
What is the eccentricity of the equation 9x² - y² - 2y - 10 = 0?
a) 1.15
b) 2.61
c) 3.16
d) 3.14
c) 3.16
A cooling tower is a hyperbolic structure. Suppose its base diameter is 100 meters and its smallest diameter of 48 meters occurs 84 meters from the base. If the tower is 120 meters high, approximate its diameter at the top.
a) 49.27 m
b) 75.30 m
c) 81.36 m
d) 60.97 m
d) 60.97 m
