# Analytic geometry - practice problems

Analytic geometry, also known as coordinate geometry, is a branch of mathematics that deals with the study of geometric shapes using the techniques of calculus and algebra. It uses a coordinate system to represent geometric shapes and equations, allowing for the use of algebraic methods to solve geometric problems. It is also used to model physical phenomena, such as the motion of objects in space.#### Number of problems found: 235

- Line - slope intercept form

What is 2x−y= 4 in slope intercept form? - Find the 12

Find the equation of the circle with center (3,7) and circumference of 8π units. - Vector

Determine coordinates of the vector u=CD if C[8;13], D[7,14]. - A circle

A circle relation is given to be x² + y² =16. What is the radius of the circle? - Place vector

Place the vector AB if A (3, -1), B (5,3) in point C (1,3) so that AB = CO. - Coordinates - rectangle

Find the perimeter of the rectangle with vertices A(1,4), B (1,0 ), C (4,0), D (4,4 ) - Distance problem 2

A=(x,2x) B=(2x,1) Distance AB=√2, find the value of x - Points collinear

Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - Segment

Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - Perpendicular

Find the slope of the line perpendicular to the line p: y = 8x +6. - The angle of lines

Calculate the angle of two lines y=-5 and y=x-23 - FX parabola

Determine the equation of the parabola going through the following co-ordinates (1;2), (-1;-2), and (2;7) - Using

Using the point-slope equation, find the equation containing (-7, 3) and slope m = -4 - Find quadrant

Point Y is located at (4, -2) on a graph. Point Z is located five units to the left of Point Y. In which quadrant is Point Z located? - Midpoint between conjugate

Find the midpoint between two roots: 2+3.464i and 2 - 3.464i - 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) - Coordinates of vector

Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5) - Parametric 82072

Convert the parametric expression of the straight line to a general equation. x=3-5t y=-4+10t - X intercept

Given: 3y+2x=-6 Calculate the X-intercept. - Three 237

Three vertices of a rectangle have the coordinates (5, 3), (5, -1), (-1, -1). What are the coordinates of the fourth vertex of the rectangle?

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