Find the equation of the sphere if one of its diameters has endpoints (3, -4, 5) and (5, 0, 11) which has been normalized so that the coefficient of x is 1. = 0.

Q: Find parametric equations for the normal line to the surfacez=-7x2 -9y2   at the point  (2,1,-37)

A:

Q: Find the equation of the circle passing through the points A(2,1), B(0,5), C(-1,2) using LU…

A:

Q: Find the length of the curve 36y2 = (x — 4)3 , 2 ≤ y ≤ 3, y ≥ 0.

A:

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

A:

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

A:

Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

A:

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

Q: By differentiating implicitly, find the slope of the hyperboloid x +y? - z = 1 in the r-direction at…

A:

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

A:

Q: Find the equations of the normal line to the surface z = at the point (1, - 2, 32). - t + 32 ||

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 the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

A:

Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Find the equation of the normal line to the paraboloid z = 2x² +y² at the point (1,2,6). Select one:…

A: Equation of paraboloid  To find: The equation of normal at a point P = (1,2,6).

Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: Evaluate the length of the curve x = 6 – Vy – 2 , 3< y<6

A: To find the length of following curve  x = 6 - sqrt( y - 6) 3 ≤ y ≤ 6

Q: find a parametrization for the curve. the line segment with endpoints (-1, -3) and (4, 1)

A:

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

A:

Q: b) Find equations for the tangent plane and normal line at the point P-(2, –3,18) on the surface…

A: x2+y-2xy-x+3y-z=-7   Let fx,y,z=x2+y-2xy-x+3y-z+7 and the point is 2,-3,18 Now,…

Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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: Find an equation of the normal line to the surface z = ye 2æy at the point (0, 2, 2).

A:

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

A:

Q: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

A:

Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)?

A: the equation of the normal line to the ellipse can be found by differentiating the given equation…

Q: Find the equation of the normal line at the point (-2,1 – 3) to the ellipsoid + y2+ 름= 3.

A: To determine the equation of the normal line.

Q: Find the equation of the sphere if one of its diameters has endpoints (3, 1, -5) and (5, 5, 1) which…

A:

Q: Find the equation of the sphere if one of its diameters has endpoints (7, -2, 8) and (9, 2, 14)…

A: Given: The sphere diameters has endpoints (7,-2,8) and (9,2,14) which has been normalized so that…

Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…

Q: Find the equation of the sphere if one of its diameters has endpoints (-5, -5, 1) and (-3, -1, 7)…

A:

Q: Find the equation of the sphere if one of its diameters has endpoints (-3, -2, -4) and (-1, 2, 2)…

A: Given: The endpoints of one of its diameter are -3,-2,-4 and -1,2,2. The coefficients of x2 is 1.

Q: Find an equation of the tangent plane to the surface at the given point. 5 —х — у, z = 5 - (3, -2,…

A:

Q: Find the equation of the plane containing the x-axis and passing through the point (4,3,1/5)

A:

Q: At what point does the normal to y = 2x2 – (3 + 2x) at (1, –3) intersect the parabola a second time?…

A: Given: y=2x2-3+2x Point: 1,-3 Objective is to find the point where the normal to y=2x2-3+2x at…

Q: Find an equation of the tangent plane to the surface at the given point. x² + y² 7z² = 138, (-8, -9,…

A:

Q: Find the minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

A:

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 normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)? O y =…

A:

Q: Find all equations of normal line at the point (1, 1, –1) to the surface 2 +z² +3 = 2y + y?…

A:

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

A:

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

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 an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find the equation of the sphere if one of its diameters has endpoints (8, -2, 8) and (11, 4, 17)…

A:

Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

A:

Q: Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

A: This is a problem of geometry. We will calculate slope of x, y and z at given point and general…