(a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (3, 2, 5) (b) Find a set of symmetric equations for the normal line to the surface at the given point. Z -4 -1 == X + 6 = y+2_zZ+5 = -1 z-5 -1 0X-3-1-2- Ox+ 3 = y + 2 =z+5 Ox-3=y-2=Z-5 =.
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- (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1, 3, 2) (b) Find a set of symmetric equations for the normal line to the surface at the given point.Find an equation of the tangent plane to the surface at the given point. X²+y²+z²=14, (1,2,3) And find a set of symmetric equation for the normal line to the surface at the given point. ○X-1/1 = y-2/2 = z-3/3 ○X-1/14 = y-2/14 = z-3/14 ○X/1 = y/2 = z/3 ○X/14 = y/14 = z/14 ○X-1 = y-2 = z-3Find parametric equations for the normal line to the surface z=-7x2 -9y2 at the point (2,1,-37)
- Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2) and find a set of symmetric equations for the normal line to the surface at the given point.A-) Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the plane 2x + 4y + 6z = 3. B-)Find the extremum and saddle points of the function f (x, y) = x^3 − 3xy + y^3 if any.Find an equation of the tangent plane to the surface y ln xz2 = 2, at the given point (e, 2, 1) and find a set of symmetric equations for the normal line to the surface at the given point.
- Find an equation of the tangent plane to the surface f(x, y) = x2y at the given point (2, 1, 4) and find a set of symmetric equations for the normal line to the surface at the given point.This is a two-part problem. I. Find the equation of the tangent plane to the surface x = 4y^2 + 3z^2 - 465 at the point (10, -10, -5). Make the coefficient of x equal to 1. II. Find the equation of the normal line to the surface x = 4y^2 + 3z^2 - 465 at the point (10, -10, -5). Make the coefficient of x equal to 1.Find the equation for the tangent plane to the surface z=-8x2 -4y2 at the point (2,1,-36)
- Find an equation of the tangent plane to the surface z = √(9 − x2 − y2), at the given point (1, 2, 2) and find a set of symmetric equations for the normal line to the surface at the given point.Find an equation of the tangent plane to the surface z = x2 + y2 + 3 at the given point( 2, 1, 8).find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2 + y2 - z2 = 18, P0(3, 5, -4)