Consider the sphere r? + y? + 22 = 9. Please find the equation of the plane tangent to this sphere at (3,0,0) (2, 2, 1)

Q: Sketch the section of the surface at x = 0. y? – 42? = 4

A: Given

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A: Given equation of curve is z = ln x The radius function about z axes is  r(z) = x = ez

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? + z? = 25 at the point…

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Q: Find the center and radius of the sphere x? – 6x – 8 + y? + 4y +z? – 20z = 0 OA C(3,-2,10), r = 11…

A: Recall: Equation of the sphere :         x-a2+(y-b)2+(z-c)2=r2; where a,b,c is the center and 'r' is…

Q: (4) Find the points Po = (xo, Yo, 2o) on the sphere x? + y? + z² = 9 so that the tangent plane to…

A: Topic- equation of tangent in 3D

Q: Find the equation of the tangent plane at the point T(1,1,4) of the sphere (x – 1)2 + (y – 2)² + (z…

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Q: Find the distance between the point and the plane.

A: The distance of a point from a plane in the standard equation form is equal to . The given point…

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: Write an equation in general form of the tangent plane to the parametric surface at the stated…

A: Equation of tangent plane

Q: Find the equation of the tangent plane to +y? at the point (2,-2,5) the surface z= 4 O r + 4y - % =…

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Q: Find the equation of the sphere with the given conditions: (a) center at (1, – 2, – 4) and its…

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Q: Find the standard equation of the sphere with center (-4, 3, 8) that is tangent to the plane given…

A: The center of the sphere is (-4,3,8) . The tangent plane is 3x+8y-4z=24 The radius of the sphere is…

Q: z = In (x² + y²) at point Po(1,0, 0).

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Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

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Q: Find the parametric equation of x, y, z where : . z2 = x2 + y2 p. 9 = x2 + y² Nhat is the name of…

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Q: b) what is the direction 8. Find the equation of the plane tangent to the surface z? = x?y + y2x+ 10…

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Q: Find the equation of the tangent plane to the surface 2² at the point Y= 2x? (0, –1,2) %3D O y- 2z…

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Q: Find the equation of the tangent plane to the surface z = 4 +y? at the point (2,-3, 10) Ox+ 4y- z =…

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Q: Consider the sphere x² + y² + z² = 9. Please find the equation of the plane tangent to this sphere…

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Q: Find an equation for the plane that is tangent to the surface z= Vy - I at the point (2, 3, 1).

A: We have to find partial derivatives first.

Q: Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 6) i+ (v³…

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Q: 1. (a) Parametrize the curve of intersection of the sphere a? + y? + 22 22 + 222 = 1, Try your best…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Write an equation of the tangent plane to the ellipsoid (a – 5)? + 4y? + 222 : М(5, 3, 1). = 38 at…

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Q: Find the equation of the tangent plane to the sphere x² + y? + z² = 1 at the point (1/ V3, 1/V3,…

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Q: Find a parameterization of the line formed by the intersection of the following planes: 1:2x-y+3z 1…

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Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: Given a sphere with center (6, 4, – 3) and radius 5. Find an equation of the intersection of this…

A: First write the equation of sphere then satisfy the condition for xz-plane.

Q: 6. Consider the sphere a2 + y? + (z-3)2 = 1. Find the point P (a, b, c) on the sphere such that the…

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Q: Find the angle between the two planes −2x + y + z = 2,  6x − 3y + 2z = 4 and find a set of…

A: The given planes are −2x + y + z = 2  and  6x − 3y + 2z = 4 . Obtain the angle between them as…

Q: Given a sphere with center (7,3, – 4) and radius 5. Find an equation of the intersection of this…

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Q: Find an equation of the tangent plane to the surface 2² + 2y? + z? = 175 at the point (5, -5, 10).

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Q: In each part, find an equation of the sphere with center (−3, 5,−4) and satisfying the given…

A: Consider the given: a) Tangent to the xy−plane:x−−32+y−52+z−−42=−42x+32+y−52+z+42=16

Q: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…

A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…

Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

Q: The two surfaces x2 + y2 + z? = 6 and 2x2 + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: We have to find angle between two tangents - First we will find divergence of function f at point…

Q: In each part, find an equation of the sphere with center (2, −1, −3) and satisfying the given…

A: Given that: Centre of sphere = (2, -1, -3)

Q: In each part, find an equation of the sphere with center (5, –8, –4) and satisfying the given…

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Q: Answer the following questions about the sphere whose equation is given by + y' + z – 6x + 10y = 2.…

A: Compare the given Equation with standard equation of sphere then find radius and center

Q: Consider the ellipsoid a? + y? + 4z2 = 12. 1. Find the general equation of the tangent plane to the…

A: We need to find the partial derivatives of the function w.r.t x,y,z for finding the equation of…

Q: Find the distance between two planes a and a1 that are tangent to the ellipsoid 2 +2y? + z² = 5/8…

A: We have to find the distance between the two tangent planes parallel to x+y+z=0  that are tangent to…

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: Find the center and radius of the sphere x? – 6x – 10+y? + 10y +z? – 20z = 0 OA C(-3,5,10), r = 10…

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

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Q: Find an equation of the plane that is normal to the surface Iz + yz? = 2+ yz at the point (2,-1, 1).

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Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Q: Consider the equation of the surface S given by -3x - 2y³z4+ xy = -4 where a and Bare pair numbers,…

A: Use formula of equation of Tangent plane

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? +z? = 25 at the point…

A: Since you have asked multiple questions in single request.so we will answering only first question.