# Analytic geometry - problems

- Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Hyperbola

Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Ellipse

Ellipse is expressed by equation 9x^{2}+ 25y^{2}- 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse. - Find the 3

Find the distance and mid-point between A(1,2) and B(5,5). - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 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[-2, -20] L[4, 1] M[-16, 4]. Calculate its area and itsinterior angles. - Speed of Slovakian trains

Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18]. - Angle between lines

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

What is the slope of a line with an inclination -221°? - Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20) - 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-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - XY triangle

Determine area of triangle given by line 7x+8y-69=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 [0,6] and touch the X-axis point [5,0]: ? - Distance

Calculate distance between two points X[18; 19] and W[20; 3]. - Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]? - Perpendicular

Determine the slope of the line perpendicular to the line p: y = -x +4. - Circle

Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes? - 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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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.