Analytic geometry + quadratic equation - math problems

Number of problems found: 25

  • Sphere equation
    sphere2.jpg 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).
  • Equation of circle 2
    circle_axes Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x.
  • Distance problem 2
    geodetka A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
  • 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?
  • 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
  • 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?
  • 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.
  • 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].
  • Distance problem
    linear_eq A=(x, x) B=(1,4) Distance AB=√5, find x;
  • Prove
    two_circles 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
  • 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].
  • 3d vector component
    vectors The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
  • 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.
  • 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
  • Find parameters
    circle_axes Find parameters of the circle in the plane - coordinates of center and radius: ?
  • 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 Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
  • Find the 15
    ellipseTangent Find the tangent line of the ellipse 9 x2 + 16 y2 = 144 that has the slope k = -1
  • 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].
  • Points in space
    roviny There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points?

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