Equation + analytic geometry - practice problems - page 4 of 6
Number of problems found: 110
- Intersection 19343
What is the sum of all coordinates of points at the intersection of the line p: x = -1-2t, y = 5-4t, z = -3 + 6t, where t is a real number, with the coordinate planes xy and yz?
- Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
- Vector equation
Let's v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7). Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1, c2, c3 and decide whether v, u, and w are linear dependent or independent
- Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14, and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
- Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation.
- Equation of the circle
Find the equation of the circle with center (3,7) and circumference of 8π units.
- Three points 4
The line passed through three points - see table: x y -6 4 -4 3 -2 2 Write line equation in y=mx+b form.
- Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
- Perpendicular and parallel
Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular and parallel lines. What angle does each line make with the x-axis, and find the angle between the lines?
- Intersection 8295
Write whether the function is ascending or descending and determine the coordinates of the intersection with the x and y axes: y = 3x-2 y = 5x + 5 y = -0.5x-1
- Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: x²+(y-3)²=14
- Midpoint 4
If the midpoint of a segment is (6,3) and the other endpoint is (8,-4), what is the coordinate of the other end?
- Coordinates of midpoint
If the midpoint of the segment is (6,3) and the other end is (8,4), what is the coordinate of the other end?
- On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
- Axial symmetry
Find the image A' of point A [1,2] in axial symmetry with the axis p: x = -1 + 3t, y = -2 + t (t = are a real number)
- Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find the value of x
- Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
- Equation of the circle
Find the equation of the circle with the center at (1,20), which touches the line 8x+5y-19=0
- Right triangle from axes
A line segment has its ends on the coordinate axes and forms a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
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