Analytic geometry - practice problems - page 4 of 14
Number of problems found: 268
- Circle point equation
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1]. - Triangle height vertices
Calculate the height of side b (v_b) of triangle ABC with vertices A[4;1;3] B[2;3;3] and C[1;1;3]. - Line parametric equation
Convert the parametric expression of the straight line to a general equation. x=3-5t y=-4+10t - Closest point
On the line p: 2x + y + 1 = 0, find the point A ∈ p that is closest to the point P =(1,0) - Equation of a circle
Write the general equation of a circle with center S(2;5) and point B(5;6) lying on this circle. - Triangle point coordinates In triangle ABC, determine the coordinates of point B if you know that points A and B lie on the line 3x-y-5=0, points A and C lie on line 2x+3y+4=0, point C lies on the x-coordinate axis, and the angle at vertex C is right.
- Line coefficient determination
In the equation of the line p: ax-2y+1=0, determine the coefficient a so that the line p: a) it formed an angle of 120° with the positive direction of the x-axis, b) passed through point A[3,-2], c) was parallel to the x-axis, d) had a direction of k = 4. - In plane 2
A triangle ABC is located in the plane with a right angle at vertex C, for which the following holds: A(1, 2), B(5, 2), C(x, x+1), where x > -1. a) determine the value of x b) determine the coordinates of point M, which is the midpoint of line segment - Triangle height intersection
Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides. - Function graph intercepts
Draw the graph of the function y = -2x + 3. Calculate the coordinates of the intersections of the function's graph with the x and y axes. - Parabola point equation Write the equation of the parabola that passes through the points: A[1,1] B[3,-1] C[1,2]
- Line - slope intercept form What is 2x−y= 4 in slope intercept form?
- Segment center coordinates
A (a1, 4) B(7, -2) segment AB has a center where both coordinates are equal - Equation of the circle
Find an equation of the circle whose diameter has endpoints (1,-4) and (3,2). - FX parabola Determine the equation of the parabola going through the following co-ordinates (1;2), (-1;-2), and (2;7)
- Tennis ball parabola
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court? - Crosswind
A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed? - The coordinates 2
The coordinates of the vertices of the triangle shown are A(1,7), B(5,2), and C(5,7). What is the length of segment AB in units? - Quadrilateral PQRS
PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it - Line integer coefficients
Good day, Even though it is a trivial task, I don’t know how to deal with it. This is analytic geometry: Find all integers a, b, and c such that the line given by the equation ax+by=c passes through the points [4,3] and [−2,1]. Thank you for your answer
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