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A circle is the locus of a point in a pl...

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle `|z-c|=a`, the equation of a sphere of radius is `|r-c|=a`, where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at `(-g, -f, -h)` is `x^2+y^2+z^2+2gx+2fy+2hz+c=0` and its radius is `sqrt(f^2+g^2+h^2-c)`. Q. Equation of the sphere having centre at `(3, 6, -4)` and touching the plane `rcdot(2hat(i)-2hat(j)-hat(k))=10` is `(x-3)^2+(y-6)^2+(z+4)^2=k^2`, where k is equal to

A

`3`

B

`4`

C

`6`

D

`sqrt(17)`

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The correct Answer is:
(b)
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A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. The centre of the sphere (x-4)(x+4)+(y-3)(y+3)+z^2=0 is

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