(a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (9, 2, 77) (b) Find a set of symmetric equations for the normal line to the surface at the given point x + 9 y + 2 z + 77 18 -4 -1 Ox - 9 = y- 2 = z - 77 OX-9 - y - 2 z - 77 18 -4 -1 Ox + 9 = y + 2 = z + 77 y -4 %3D %3! 18 -1
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- 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-3(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.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 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.Consider the surface x2 + y2 − 2xy − x + 4y − z2 + 4 = 0 at the point Po (2, −2, 5). Determine the following:(a) the general equation of the tangent plane to the surface at Po(b) the parametric equations of the normal line to the surface at Po
- 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.find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2 + y2 - 2xy - x + 3y - z = -4, P0(2, -3, 18)Find the point of intersection between the surface y=9 and the tangent line to the curve of intersect at the point (-3,0,3) of the following two surfaces given z > 0. x2+y2+z2=18 z2=x2+y2
- Let ƒ(x, y) = x2 + y3. Find the slope of the line tangent to this surface at the point (-1, 1) and lying in the a. plane x = -1 b. plane y = 1.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.The plane y = 1 intersects the surface z = x^4 + 6xy − y^4 in a certain curve. Find the slope of the tangent line to this curve at the point P = (1, 1, 6).