An equation of sphere with centre at origin and radius r can be r… - Vidyadip

MCQ

An equation of sphere with centre at origin and radius r can be represented as:

A
$x^2+y^2+z^2=r$
✓
$x^2+y^2+z^2=r^2$
C
$x^2+y^2+z^2=2 r^2$
D
None of the above

✓

Answer

Correct option: B.

$x^2+y^2+z^2=r^2$

$x^2+y^2+z^2=r^2$

Solution:
Sphere is locus of a point in 3D whose distance from a fixed point (center) is constant (radius)
$\Rightarrow\sqrt{({\text{x}-0})^2+(\text{y}-0)^2+(\text{z}-0)^2}$
$=\mid\text{r}\mid\Rightarrow\text{x}^2+\text{y}^2+\text{z}^2=\text{r}^2$ square both sides.

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