. Suppose that A = 2, 5 are the coordinates of a point inthe xy-plane (a) Find the coordinates of the point if A is shifted 3 units tothe left and 4 units down.(b) Find the coordinates of the point if A is shifted 2 units tothe left and 8 units up.

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

A:

Q: Which of the following is the equation of the plane that is tangent to the surface 2 x² + y? – x z –…

A: Consider the provided information, The provided surface, 2x2+y2-xz-3z=1 Find the partial derivative…

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

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

A: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

Q: Find the equation of the plane tangent to the following surface at the given points. x² +…

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Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

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

Q: Which of the following is the equation of the tangent plane to the surface z = 3x2 +x-y²+y at the…

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Q: (42) is the distance between the point (1, –3, –2) and the plane x- 4y-3z-2= 0.

A: In this question we have to find the distance between point and plane. Note: As per our policy we…

Q: Find an equation of the plane tangent to the following surface at the given point. z= 6- 3x - 2y;…

A: The equation of tangent plane to the surface z=fx,y at the point a,b,fb can be calculated using the…

Q: Find the distance from the plane given by 6x − 2y + 3z − 1 = 0 to the point (4, 1, 3).

A: The distance from plane to a point is given by  d=Ax1+By1+Cz1+DA2+B2+C2 Where Plane is Ax+By+Cz+D=0…

Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

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Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: Which of the following is the equation of the plane that is tangent to the surface 2 x2 + y? x z –…

A: Given: 2x2+y2-xz-3z=1

Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

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Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

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Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

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Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: 7. If 1x, y2 are the coordinates of a point P in the xy-plane,then x is called the__________________…

A: Given that, x,y are the coordinates of a point P in the xy-plane. The objective is to fill in the…

Q: The distance from the point P(1,2,3) to the plane x +y + z = 0 is

A:

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

A:

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: Find the equation of the plane tangent to the following surface at the given points. 2 x +y -z - 52…

A: See the details solution in below

Q: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

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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: Calculate y°dz – yz²dy – sen(2)dz, where C'is the path connecting the point A(-2, 2, 4) to the point…

A: We will calculate the integral ∫Cy2dx-yz2dy-sinzdzwhere path starts from point A-2,2,4 to the point…

Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

A:

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: Find an equation of the plane tangent to the following surface at the given point. z= 3- 3x -y:…

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Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

A:

Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Find the distance from the point (1, 1, 1) to the plane x + 2y + 3z  = -4

A:

Q: the

A: We will find the distance.

Q: find an equation for the plane that is tangent to z=4x^2+y^2 at the point (1,1,5)

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Q: Find the distance between the point and the plane. (0, 0, 0) 2x + 6y + z = 12

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Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: Find the distance from the point (0,8,9) to the plane – 2y + 3z = 11.

A: In this question, we will find the distance from the given point to the given plane.

Q: Find the distance from (.-4,5) to each of the following. (a) the xy-plane (b) the yz-plane (c) the…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Q2) Find the distance from the point P (1, 2, 3) to the plane x-3y + 2z= 4.

A:

Q: Find the equation of the tangent plane to the surface x?+ Qy?-322=3' at (2-1,1) x²+ 2y 2-322=3'at…

A: Equation of a tangent plane

Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

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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

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.