# Quadratic equation + analytic geometry - math problems

#### Number of problems found: 24

- Sphere equation

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

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

A=(x,2x) B=(2x,1) Distance AB=√2, find value of x - Curve and line

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

Find the intersections of the circles x^{2}+ y^{2}+ 6 x - 10 y + 9 = 0 and x^{2}+ y^{2}+ 18 x + 4 y + 21 = 0 - Suppose

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

From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x_{0}, y_{0}] and radius of the circle r. - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - Prove

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: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - On a line

On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - On line

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]. - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - 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 - Find parameters

Find parameters of the circle in the plane - coordinates of center and radius: ? - Circle

Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ? - Circle

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

Find the tangent line of the ellipse 9 x^{2}+ 16 y^{2}= 144 that has the slope k = -1 - Tangents to ellipse

Find the magnitude of the angle at which the ellipse x^{2}+ 5 y^{2}= 5 is visible from the point P[5, 1] . - Points in space

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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