Equation of a...

Equation of a Sphere : General Form

Trending Questions

Q. The center of the circle given by

\to r \cdot (^i + 2^j + 2^k) = 15

and

| \to r - (^j + 2^k) | = 4

Q. A line passes through the centre of a sphere whose radius is 5 and one of the intercept points is

(1, - 2, 2)

. If the equation of the line is

\frac{x}{1} = \frac{y}{- 2} = \frac{z}{2}

, then the equation of the sphere can be

$x^{2} + y^{2} + z^{2} - \frac{16}{3} x + \frac{32}{3} y - \frac{32}{3} z = - 39$
$x^{2} + y^{2} + z^{2} + \frac{4}{3} x - \frac{8}{3} y + \frac{8}{3} z - 21 = 0$
$x^{2} + y^{2} + z^{2} + \frac{16}{3} x - \frac{32}{3} y + \frac{32}{3} z = - 39$
$x^{2} + y^{2} + z^{2} - \frac{16}{3} x + \frac{32}{3} y - \frac{32}{3} z = 39$

Q. Let any tangent plane to the sphere

(x - a)^{2} + (y - b)^{2} + (z - c)^{2} = r^{2}

makes intercepts

a, b, c

with the coordinate axes at

A, B, C

respectively. If

P

is the centre of the sphere, then

(

a r .

and

v o l .

denote the area and volume respectively

)

Q. The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere

x^{2} + y^{2} + z^{2} + 4 x - 2 y - 6 z = 155

Q. A line passes through the centre of a sphere whose radius is 5 and one of the intercept points is

(1, - 2, 2)

. If the equation of the line is

\frac{x}{1} = \frac{y}{- 2} = \frac{z}{2}

, then the equation of the sphere can be

$x^{2} + y^{2} + z^{2} - \frac{16}{3} x + \frac{32}{3} y - \frac{32}{3} z = - 39$
$x^{2} + y^{2} + z^{2} + \frac{4}{3} x - \frac{8}{3} y + \frac{8}{3} z - 21 = 0$
$x^{2} + y^{2} + z^{2} + \frac{16}{3} x - \frac{32}{3} y + \frac{32}{3} z = - 39$
$x^{2} + y^{2} + z^{2} - \frac{16}{3} x + \frac{32}{3} y - \frac{32}{3} z = 39$