1. Consider the ellipsoid x² + y² + 4z? = 12. (a) Find an equation of the tangent plane to the ellipsoid at the point (2, 2, 1). = 12.

Q: Find the area of the surface generated when the curve y [2,4] is rotated about the y-axis.

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Q: EXAMPLE 9 Find the tangent plane to the surface with parametric equations x = u2, y = v2, z = u + 2v…

A: Given parametric equation x=u2 , y=v2 , z=u+2v

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: 3. Find the equation of the tangent plane to the given surface at the point (0,-1,-2). y = 2x? - ? O…

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Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = ln (x2 +…

A: The given function is It can be written as as the given function has both variables x and y.

Q: (4) The equation of the tangent plane to the surface In = z²(x – 2y) + 3z +3 at (4, 2, –1) is 2y

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Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

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Q: Find a point on the ellipsoid x² + 2y2 + z2 = 19 where the tangent plane is perpendicular to the…

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Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the…

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Q: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

Q: Find an equation of the plane tangent to the surface sin(xyz) = at the point (T, 1,-)

A: sinxyz=12 at the point π, 1, 16. Consider, sinxyz=12⇒xyz=sin-112⇒xyz=π6⇒z=π6xy Differentiating…

Q: Find equation of the tangent plane to the given surface at the specified point. 5x^2+3y^2+8z^2,…

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Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

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Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.

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Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

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Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

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Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

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Q: Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line…

A: Given  The equation of ellipsoid is given by fx,y,z=x2+4y2+z2-9 The line is x=2-4t, y=1+8t and…

Q: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

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Q: Find an equation of the tangent plane to the given surface za² + y² +1 at (1,1,3).

A: Given equation of the surface is  z=x2+y2+1 We have to find the tangent plane of the given surface…

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

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Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: 2. Let a, b, and c be three nonzero constants. Show that the equation of the tangent plane to the…

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Q: 22 2 Find the equation of the tangent plane to the level surface xy*z? (– 1, – 1, – 2) = 4 at the…

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Q: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

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Q: determine a and b as to make the cylinder y^2=4ax orthogonal to the ellipsoid at point (1,2,1)

A: Given equation of the cylinder is  y2=4ax, say φ1=y2-4ax=0 and the general equation of the ellipsoid…

Q: Consider the ellipsoid x2+ y2+ 4z2= 12. Find the general equation of the tangent plane to the…

A: Given that the ellipsoid x2 + y2 + 4z2 = 12. We find the general equation of the tangent plane to…

Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – z2 O y…

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Q: Find the equation of the tangent plane at the point (-2,1 – 3) to the ellipsoid surface + y? + = 3.

A: Find the equations of the tangent plane and normal line at the point (-2, 1, -3) to the ellipsoid…

Q: 3. Find an equation of the tangent plane to the surface z = 2xy + 4y xy-2x at the point (1,1,-6)

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Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Find the equation of the plane tangent to and the line (in symmetric form) normal to the ellipsoid…

A: Given:   x2+ 4y2 +8z2 = 48 Point : ( -2 , 3 , -1)

Q: At what point on the ellipsoid 2x^2 + y^2 + z^2 = 1 is the tangent plane parallel to the plane x + y…

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Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of…

A: Given that the curve of intersection of the parabolic cylindery=x2 and the top half of the ellipsoid…

Q: Show that the ellipse x = a cos t, y = b sin t, a > b > 0, has its largest curvature on its…

A: Consider the given equation as x=acost, y=bsint and a>b>0

Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

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Q: Show that the ellipse x = a cos t, y = b sin t, a> b>0, has its largest curvature on its major…

A: The curvature for a parametrized curve c(t) = x(t)i + y(t)j is :

Q: Find the equation of the tangent plane to the surface 4. =1 at the point 16 9. (1,-3,2) O a.…

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