Analytic geometry - practice problems - page 2 of 13
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: 248
- A linear
A linear function has a y-intercept of -12 and a slope of 3/2. What is the equation of the line? - Line segment
Find the length of the line joining points A(-4,8) and B(-1,4). - The linear
The linear equation 5y-3x-4=0 Can be written in the form y=mx+c. Find the values of m and c. - Find all 2
Find all the complex solutions (write the answer in the form x+iy) of the system. {|z-12|/|z-8i|=5/3 ; |z-4|=|z-8| - At noon 3
At noon, the temperature was 45˚ F. For the next ten hours, the temperature fell at a steady rate. The graph represents the temperature every hour since noon. At 5:00 temperature was 20°F. At what rate did the temperature fall? - Midpoint between conjugate
Find the midpoint between two roots: 2+3.464i and 2 - 3.464i - Slope of line
What is the slope of the line that passes through the points: (-2, 4) and (-3, 1)? - Calculate 83160
Calculate the distance of point A[ 4; 2; -3 ] from the plane : 2x - 2y + z + 5 = 0 - Coordinates 83025
Given are points A [1;a2;a3], B [3;-4;-1], C [-3;-1;8]. Points A, B, and C lie in a straight line. Calculate the coordinates a2, a3 - Determine 83003
Determine the value of the number a so that the graphs of the functions f: y = x² and g: y = 2x + a have exactly one point in common. - Perpendicular 82994
The straight line p is given by the formula y = 1/2 x - 1 . The line q is perpendicular to the line p and passes through the point A [1; 5]. Determine the y-coordinate of the point that intersects the line q with the y-axis. - Calculate 82992
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - Parametrically 82990
Calculate the sum of the x-coordinates of the intersections of the circle given by the equation (x - 1)²+ y² = 1 and the line given parametrically x = t, y = t , where t∈R. - Coordinate 82855
What is the ratio of the distance of the nearest and farthest point of the circle described by the equation x2+y2-16x-12y+75=0 from the origin of the coordinate system? - Vertex of the rectangle
Determine the coordinates of the vertex of the rectangle inscribed in the circle x²+y² -2x-4y-20=0 if you know that one of its sides lies on the line p: x+2y=0 - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - The tangent of the hyperbola
Write the equation of the tangent of the hyperbola 9x²−4y²=36 at the point T =[t1,4]. - Coordinate 82580
Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4]. - Calculate 82578
The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A. - Right-angled 82561
Determine point C so that triangle ABC is right-angled and isosceles with hypotenuse AB, where A[4,-6], B[-2,10]
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