Question

6. Determine any points where the curve given by C :=t, y = ta, z = + intersects the cylinder y = 16-22. If no such points exist, state this.

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Answer 1

(Ans) Given the curve C: x=t , y=t^2 and z=t^3.

Now to determine the points where the given curve intersects the cylinder y= 16 - x^2--->(1).

By substituting the x and y values inin the cylinder equation, we get

t^2 = 16 - t^2.

2t^2 = 16.

t= +2√2 and -2√2.

Now the values of x,y and z for the above values of t are given below.

For t=2√2 then x=2√2 , y=8 and z= 16√2.

For t=-2√2 then x=-2√2, y=8 and z= -16√2.

Therefore the points of the given curve to intersect the cylinder are given below.

(x,y,z) points are ::

(2√2, 8 , 16√2) and (-2√2, 8 , -16√2).

I hope it is clear. Thank you. Please support me with a like.