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).

Correct answer:

r =  3.9398
x₀ =  1.4894
y₀ =  1.1915
z₀ =  -2.234

Step-by-step explanation:

$$\begin{gathered} 3x+2z=0 \\ 4x-5y=0 \\ {r}^2=(x-0{)}^2+(y+2{)}^2+(z+4{)}^2 \\ {r}^2=(x-2{)}^2+(y+1{)}^2+(z-1{)}^2 \\ (x-x_0{)}^2+(y-y_0{)}^2+(z-z_0{)}^2=r^2 \\ r>0 \\ r=\sqrt{34289}\mathrm{/}47=3.9398 \end{gathered}$$

$x_0=70\mathrm{/}47=1.4894$

$y_0=56\mathrm{/}47=1.1915$

$z_0=-105\mathrm{/}47=-2.234$

Try another example

Related math problems and questions:

• Sphere from tree points
  Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
• 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].
• 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].
• Function 3
  Function f(x)=a(x-r)(x-s) the graph of the function has x- intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s.
• 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: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
• Quadrilateral 2
  Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
• Right triangle from axes
  A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
• Coordinates
  Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
• Intersections 3
  Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0
• Isosceles triangle
  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.
• Touch x-axis
  Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
• General line equations
  In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the line is given by the slope form: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) t
• 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
• Vertices of a right triangle
  Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
• Hyperbola
  Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
• Ellipse
  Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
• Calculate 6
  Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].