4. Find the distance from (1, −4, 9) to each of the following. (a) the xy-plane (b) the yz-plane (c) the xz-plane (d) the x-axis (e) the y-axis (f) the z-axis

Q: For numbers 1-2, consider a plane bounded by the curves y=9-x² and y=x+3. 1. What is the desired…

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Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: How do I do this?

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Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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Q: A________ is the set of points P in the plane such that the ratio of the distance from a fixed point…

A: The conic section is known as the set of points, in which the curve of any of the conic, that are,…

Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

Q: Find the distance from (2, -7, 8) to each of the following. (a) the xy-plane (b) the yz-plane (c)…

A: Here we find the distance from 2,-7,-8 to a xy plane b the yzplane , c the xz plane d the x-axis e…

Q: Find the distance from (4, –2, 6) to each of the following. a. The xy-plane

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Q: Find the points on the graph of z = xy + 8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

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Q: 5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b.…

A: Given: (a). two lines l1 and l2 (b). Two Planes (c). A point (1,2,3) and a line  To Find: (a).…

Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

A:

Q: Find the distance from the point (−5,2,−3) to the (a) xy-plane (b) xz-plane (c) yz-plane (d) x-axis…

A: We know that distanced of xy-plane from the pointx0,y0,z0 is given by d=z0…

Q: Use Eq. (8) to find the distance from Q = (1, 1, 1) to the plane2x + y + 5z = 2.

A: Find the distance from Q=(1, 1, 1) to the plane 2x+y+5z=2 or 2x+y+5z-2=0.…

Q: A sphere of constant radius r passes through the origin O, and cuts the axes in A, B, C. Prove that…

A: Given: Equation of the sphere with origin at O x2+y2+z2-ax-by-cz=0→1The radius of the sphere is…

Q: 22 Prove that the line Z=2+46 is perpendicular to thme plane X-2y+2=6

A: As per our guideline we are supposed to do 1 question at a time. Please post other questions next…

Q: 14) Determine the distance between the parallel planes: 6z = 4y – 2x; and 9z = 1 – 3x + 6y.

A: Given:-planesP1: 6z=4y-2x2x-4y+6z=0x-2y+3z=0P2: 9z=1-3x+6y3x-6y+9z=1x-2y+3z=13To find : distance…

Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

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 points on the graph of z = xy +8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

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Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

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: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Find the distance between the given parallel planes. 4x – 5y + z = 16, 8x – 10y + 2z = 3

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Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

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Q: Find the shortest distance between the point A(2, 5, –7) and the plane 3x – 5y + 6z = 9.

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

Q: Find the distance from (2, –7, 8) to each of the following. (a) the xy-plane (b) the yz-plane (c)…

A: Hey, since there are multiple subparts posted, we will answer three subparts. If you want any…

Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

A:

Q: Find the distance from (2, -2, 9) to each of the following. (a) the xy-plane (b) the yz-plane (c)…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

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Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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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

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Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: 14) Determine the distance between the parallel planes: 6z = 4y - 2x; and 9z = 1- 3x + 6y.

A: Given problem:- Determine the distance between the parallel planes: 6z = 4y - 2x and 9z = 1 - 3x +…

Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

A: Given: y=-231  and u=1-12 To compute: the distance from y to the line through u and the origin.…

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: 3. Find the shortest distance from the origin to the plane x – 2y – 2z = 3. |-

A: Here I am attaching image so that you understand each and every step.

Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

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 the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…

Q: Q2. A. Show that the plane 3x +y- z = 9 and the line {x 2,y =-1+ 3t,z 1+ 3t} are parallel, then find…

A: Answer

Q: 2 Let w = z². Find the image of the first quadrant in z-plane

A:

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.