Analytic geometry + expression of a variable from the formula - practice problems - last page
Number of problems found: 35
- ABCDEFGHIJKL 8426
The given is a regular hexagonal prism ABCDEFGHIJKL, which has all edges of the same length. Find the degree of the angle formed by the lines BK and CL in degrees. - Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: x²+(y-3)²=14 - Symmetry by plane
Determine the coordinates of an image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0 - 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].
- Center of line segment
Calculate the distance of point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t; t is from interval <0,1>. - 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 real number) - 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? - Ellipse
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the ellipse's center.
- Two forces
The two forces, F1 = 580N and F2 = 630N have an angle of 59 degrees. Calculate their resultant force, F. - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Equation of circle 2
Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x. - Circle - AG
Find the coordinates of the circle and its diameter if its equation is: x² + y² - 6x-4y=36 - Equation of circle
Find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
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