Analytic geometry - math word problems - page 12 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
- Circle
The circle is given by center on S[-7; 10] and maximum chord 13 long. How many intersect points have a circle with the coordinate axes? - Center of gravity
The mass points are distributed in space as specified by coordinates and weight. Find the center of gravity of the mass points system: A1 [1; -20; 3] m1 = 46 kg A2 [-20; 2; 9] m2 = 81 kg A3 [9; -2; -1 - Square side
Calculate the length of the side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0. - Lie/do not lie
The rule f(x) = 8x+16 gives the function. Find whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for your answer.
- Parabola
Find the equation of a parabola that contains the points at A[10; -5], B[18; -7], C[20; 0]. (use y = ax²+bx+c) - Linear independence
Determine if vectors u=(-4; -10) and v=(-2; -7) are linear dependents. - Unit vector 2D
Find coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10]. - Vector
Determine coordinates of the vector u=CD if C[12;-8], D[6,20]. - XY triangle
Determine the area of a triangle given by line 7x+8y-69=0 and coordinate axes x and y.
- Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles. - Segment
Calculate the segment AB's length if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - Circle
The circle touches two parallel lines, p, and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Center
Calculate the coordinates of the circle center: x² -4x + y² +10y +25 = 0 - Perpendicular
What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
- Cone
If the segment of the line y = -3x +4 that lies in the first quadrant is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Distance
Calculate the distance between two points K[6; -9] and G[5; -1]. - Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r² - Slope
What is the slope of a line with an inclination 3.96 rad? - Perpendicular
Find the slope of the line perpendicular to the line p: y = 8x +6.
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