The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes th

Question

The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes th

The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

Related Questions

A sphere of constant radius `k ,` passes through the origin and meets the axes at `A ,Ba n d Cdot` Prove that the centroid of triangle `A B C` lies on

2 Answers 4 Views

A variable plane passes through a fixed point `(alpha,beta,gamma)` and meets the axes at `A ,B ,a n dCdot` show that the locus of the point of interse

2 Answers 5 Views

A sphere of constant radius `2k` passes through the origin and meets the axes in `A ,B ,a n dCdot` The locus of a centroid of the tetrahedron `O A B C

2 Answers 4 Views

A line with positive direction cosines passes through the point P(2, – 1, 2) and makes equal angles with the coordinate axes. The line meets the plane

2 Answers 6 Views

Statement-I : If x and y are the distance along x and y axes respectively then the dimensions of `(d^(3)y)/(dx^(3))` is `M^(0)L^(-2) T^(@)` Statement-

2 Answers 4 Views

Find the equation of the straight line that (i)makes equal intercepts on the axes and passes through the point (2;3) (ii) passes through the point (-5

2 Answers 6 Views

Let points A,B and C lie on lines y-x=0, 2x-y=0 and y-3x=0, respectively. Also, AB passes through fixed point P(1,0) and BC passes through fixed point

2 Answers 11 Views

Normal is drawn at one of the extremities of the latus rectum of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` which meets the axes at points `Aa n dB` .

2 Answers 4 Views

The number of integral points (x,y) (i.e, x and y both are integers) which lie in the first quadrant but not on the coordinate axes and also on the st

2 Answers 5 Views

Line AB passes through point (2,3) and intersects the positive x and y-axes at A(a,0) and B(0,b) respectively. If the area of `DeltaAOB` is 11. then t

2 Answers 6 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

We are given the extremities of the diameter as (0, 2, 0) and (0, 0, 4). Therefore, the equation of the sphere is `(x-0)(x-0)+(y-2)(y-0)+ (z-0)(z-4)=0`
`or x^(2)+y^(2)+z^(2)-2y-4x=0`.
This sphere clearly passes through the origin.

6 views Answered 2023-02-05 15:29