Square (second power, quadratic) + analytic geometry - practice problems - last page
Number of problems found: 115
- 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) - 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]. - 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]. - 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]? - 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
- Line
Line p passes through A[5, -3] and has a direction vector v=(2, 3). Is point B[3, -6] on the line p? - Center
In the ABC triangle is point D[1,-2,6], which is the center of the |BC|, and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z]. - Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the center of the circle S[x0, y0] and the radius of the circle r. - Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Forces
In point, O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.
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