Rectangular Coordinates

Problem
Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.

A.   $x^2 + y^2 + z^2 - 9 = 0$
B.   $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$
C.   $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$
D.   $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$

 

Length of Arc in XY-Plane | Applications of Integration

Arc Length in xy-Plane | Derivation of Formulas | Integral Calculus

The length of arc in rectangular coordinates is given by the following formulas:

$\displaystyle s = \int_{x_1}^{x_2} \sqrt{1 + \left( \dfrac{dy}{dx} \right)^2} \, dx$   and   $\displaystyle s = \int_{y_1}^{y_2} \sqrt{1 + \left(\dfrac{dx}{dy} \right)^2} \, dy$

 

length-of-arc-xy-plane.jpg

 

See the derivations here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-xy-plane-...
 

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