Question

Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere

Answer 1

Answer:

The  parametrization,  of the given curve is  $x = 10 cos(t) \ \ ,z = 10 sin(t)$

Step-by-step explanation:

From the question we are given the function

        $x^2 + y^2 + z^2 = 125$

At  y= 5

       $x^2 + 5^2 +z^2 =125$

       $x^2 + z^2 = 100$

       $x^2 + z^2 = 10^2$

Converting the above  to it polar equation we have  

       $x = 10 cos(t) \ \ ,z = 10 sin(t)$