# Pythagorean theorem + analytic geometry - math problems

#### Number of problems found: 62

• 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].
• Three points Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
• Calculate 6 Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
• Unit vector 2D Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
• 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].
• 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. ..
• Calculate 7 Calculate the height of the trapezoid ABCD, where coordinates of vertices are: A[2, 1], B[8, 5], C[5, 5] and D[2, 3]
• On a line On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
• Perpendicular projection Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0.
• 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.
• Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
• Diameter If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
• Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
• Center of line segment Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
• Chord BC A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
• Inscribed circle Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
• 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
• Isosceles triangle In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
• Equation of circle 2 Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
• Medians and sides Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.

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For Basic calculations in analytic geometry is a 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. Pythagorean theorem is the base for the right triangle calculator.