3. The plane in ' with equation 4x=34 %3D

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

A:

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

Q: Find the equation for the tangent plane at the point Po = (1,2, 2) on the surface x + 4y2 + 22 = 25.…

A: Equation of the Surface x2+4y2+2z2=25 point 1,2,2

Q: Find the radius of curvature of a parabola y² - 4x = 0 at the point (4,4). 2

A:

Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

A:

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

A:

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Find an equation of the tangent plane to the surface given by z² – 2x2 – 2y? = 12 at the point (1,…

A:

Q: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: Ir te line x34+2¢, もー4t paralled he plane 3x +y+そこ子-

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

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

A:

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

A:

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

A:

Q: Find parametric equations of the normal line to the surface z = + y? at the point (2, -2,5) x = 2 -…

A: Let F(x,y,z) define a surface that is differentiable at (x0,y0,z0) then the normal line to F(x,y,z)…

Q: 6 of 19 Write the equation of a circle with centre (-8,-3) which is tangent to the x-axis. O (x –…

A: A detailed solution is given below

Q: Find parametric equations of the normal line to the surface z = 4 + y² at the point (2, –2, 5) |

A:

Q: 3. Find the area of the surface generated by revolving the curve y = 2/x ,1Sx<2, about the x-axis(as…

A:

Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: dy Use the method of isoclines to draw several solution curves for the equation dr

A: First integrate the function using variable separation method and find y as function of x  Then draw…

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: Let LL be a tangent line to the hyperbola xy=8 at x=7. Find the area of the triangle bounded by L…

A:

Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

A:

Q: 4) Find the families of lines of curvature of the surface : =+ y² .

A: Given: z=x2+y2

Q: 4. If the curve y = 3 – x², 0<x<4 is rotated about the y-axis, find the area of the resulting…

A:

Q: Find the equations of the normal line to the surface z = 2x°y* at the point (2, 2, 256). y = 2 = -t…

A:

Q: 13. Find an equation for the tangent plane and the normal line to the surface x? + 2y? - 3z? = 3, at…

A:

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

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

A: Solved below...

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Find the equations of the tangent plane and normal line to the surface with equation 9y? + 9z2 = 22…

A:

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: 3. Use traces to sketch and identify the following surface 25x2 + 4y² + z2 = 100.

A: Consider the given: Given:25x2+4y2+z2=100Let x=k∴25x2+4y2+z2=100             4y2+z2=100−25x2Hence,…

Q: Find an equation of the tangent plane to the given surface at the specified poin 8x2 + y2 - 7y, (1,…

A:

Q: Find the equation of the sphere of radius 7 centered at (3, 5, 3). O (x – 3) + (y– 5 + (z - 31 = 7 O…

A: Let's find.

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: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

A:

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

A: Consider the function fx,y,z=x2+y2-z2-18. ∇fx,y,z=fx, fy, fz=2x, 2y, -2z. At 3, 5, -4, ∇f3, 5,…

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &amp;…

Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.