# Analytic geometry - examples

For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.- Forces

In point X acts three orthogonal forces: F_{1}= 13 N, F_{2}= 8 N and F_{3}= 15 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles. - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12]. - Speed of Slovakian trains

Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37 - Angle between lines

Calculate the angle between these two lines: ? ? - Slope

What is the slope of a line with an inclination 1.06 rad? - Circle

Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: -x+3y+1 = 0 q: x-3y-1 = 0 a: -10x-3y-2 = 0 - Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16) - XY triangle

Determine area of triangle given by line -7x+7y+63=0 and coordinate axes x and y. - Circle

From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x_{0}, y_{0}] and radius of the circle r. - Circle

Write the equation of a circle that passes through the point [0,8] and touch the X-axis point [2,0]: ? - Distance

Calculate distance between two points Z[7; -9] and U[-10; -8]. - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-9,-8] and B[-8,0]? - Circle

Circle is given by centre on S[-9; 4] and maximum chord 20 long. How many intersect points have circle with the coordinate axes? - Center

Calculate the coordinates of the circle center: ? - Cone

If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Center

In the triangle ABC is point D[-8,-9,9], which is the center of the |BC| and point G[5,9,5], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z]. - Perpendicular

Determine the slope of the line perpendicular to the line p: y = 9x +7. - Linear independence

Determine if vectors u=(3; -3) and v=(0; 3) are linear Linear dependent. - Line

Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.

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