Analytic geometry + quadratic equation - math problems

Also known as coordinate geometry or Cartesian geometry.

Number of problems found: 24

  • Circle
    circles From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
  • Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  • Equation of circle 2
    circle_axes Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
  • Distance problem 2
    geodetka_1 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
  • Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  • Sphere equation
    sphere2 Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
  • Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  • Circle
    circles_2 Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
  • On line
    primka On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
  • Find the 15
    ellipseTangent Find the tangent line of the ellipse 9 x2 + 16 y2 = 144 that has the slope k = -1
  • On a line
    linearna On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
  • Curve and line
    parabol The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
  • Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  • Intersections 3
    intersect_circles Find the intersections of the circles x2 + y2 + 6 x - 10 y + 9 = 0 and x2 + y2 + 18 x + 4 y + 21 = 0
  • 3d vector component
    vectors_1 The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
  • Isosceles triangle
    rr_triangle3 In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
  • Tangents to ellipse
    ellipseTangent Find the magnitude of the angle at which the ellipse x2 + 5 y2 = 5 is visible from the point P[5, 1] .
  • Circle
    kruznica 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
  • Prove
    two_circles_1 Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
  • Suppose
    linear_eq Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



For Basic calculations in analytic geometry is a helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. Looking for help with calculating roots of a quadratic equation? See also more information on Wikipedia.