Hi everyone, I was solving this question however I have some doubts about the correctness of my answer:
Question:
Given a surface having the following parametric equations;
x=u
y=v
z=u2-v2-4
Determine:
1)Point Q, intersection of the surface to the positive x-axis,
2)A Cartesian equation for the plane tangent at Q to the surface
My answer for the first question: if the surface intersects the positive x-axis,
then: y=0 and z=0,
then: v=0
and
u2-v2-4=0 → u2=4 → u=2 since the surface intersects the positive x-axis.
Since u=2 and v=0, we have:
x=2
y=0
z=0
So the point Q=(2,0,0)
My answer for the second question: Since
x=u and y=v, then:
z=x2-y2-4 → "x2-y2-z-4=0" is the Cartesian equation for the plane tangent at Q to the surface.
You would be really helpful if you could point out any mistakes that I did.
Question:
Given a surface having the following parametric equations;
x=u
y=v
z=u2-v2-4
Determine:
1)Point Q, intersection of the surface to the positive x-axis,
2)A Cartesian equation for the plane tangent at Q to the surface
My answer for the first question: if the surface intersects the positive x-axis,
then: y=0 and z=0,
then: v=0
and
u2-v2-4=0 → u2=4 → u=2 since the surface intersects the positive x-axis.
Since u=2 and v=0, we have:
x=2
y=0
z=0
So the point Q=(2,0,0)
My answer for the second question: Since
x=u and y=v, then:
z=x2-y2-4 → "x2-y2-z-4=0" is the Cartesian equation for the plane tangent at Q to the surface.
You would be really helpful if you could point out any mistakes that I did.