Find the points on the hyperboloid $9x^2−45y^2+5z^2=45$ where the tangent plane is parallel to the plane $x+5y−2z=7.$
Much appreciate if someone could solve this question, thanks!
2026-02-22 21:01:23.1771794083
Find the points of a hyperboloid where the tangent plane is parallel to a plane
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HINT
For the surface $f(x,y,z)=9x^2−45y^2+5z^2=45$ evaluate
$$\nabla f(x,y,z)=(f_x,f_y,f_z)$$
which is orthogonal to $f$ in $P(x,y,z)$ and compare with the normal vector of the given plane $(1,5,-2)$.