Y is the midpoint of XZ.X has coordinates (3, 4), and Y has coordinates (-1, 9). Find the coordinates of Z.

Q: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

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Q: a) Eliminate the parameter to find equation for..! a Cartesiar X = 2t -1, y=#t+|

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

Q: Find the midpoint M of CD M = (, ) X1+X2 Y1 %3D 21 C = (-2,-10) D = (-6,0) M = ([ ? ], [ ]) Enter…

A: Explanation of the answer is as follows

Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

A:

Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

A:

Q: Y is the midpoint of XZ and V is the midpoint of WZ. If VY = 32, what is WX? WX Submit

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Q: Q1/ Find the angle between the planes 3 x -6y - 2z = 15 and 2 x +y– 2z = 5

A: Explanation of the answer is as follows

Q: Find the coordinates of the midpoint of HX 1 ,-3 2' X 2

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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 the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

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Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find the length of the curve y = x2, 0 ≤ x≤√3/2.

A:

Q: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

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Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

A:

Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: Convert to standard from and give the center and radius: x^2+ Y^2 - 2x +6y - 1=0

A: x-h2 +y-k2 =r2 (h , k) is centre and r is radius .

Q: Determine the location of a point (x, y, z) that satisfies the condition y < 0

A: With the given condition there are 4 scenarios 1) x>0,y<0,z>0 2) x<0,y<0,z<0 3)…

Q: Find the length of the curve x y? – 2y, 0< y < 2.

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Q: Find the distance from the point (1, 2, 0) to the line æ = 3t, y= 1, z= 2 – t.

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Q: Find the midpoint of these two points (4, 6) and (7, 10) Use the formulas: x = (x1 + x2)/2 %3D y (yi…

A: Consider the points, 4,6      and         7,10 The midpoints of two points is given by the formula,…

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

Q: Eliminate the parameter from x = 2sint, y=4cost

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Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

A:

Q: Q4/ Find the angle between the curves x² = y & y² = x

A: The curves intersect at (1,1).  Now calculate slope at (1,1):  ddxx21,1=ddxy1,12x1,1=dydx1,1m1=2…

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: PQ lies in the standard (x, y) coordinate plane. What are the coordinates of the midpoint of PQ if P…

A: We need to find the coordinates of the midpoint of PQ¯ if P is located at -7,-11 and Q is located at…

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: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

Q: find the distance from the point to the plane. (0, 1, 1), 4y + 3z = -12

A: we have to find the distance of the point (0,1,1) from the plane 4y+3z=-12.   as we know that the…

Q: Find the acute angle between the planes x = 7 and x + y + √2z = -3.

A: Acute angle between two planes a1x+b1y+c1z+d1=0 and a2x+b2y+c2z+d2=0 is,…

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

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Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

A:

Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

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Q: Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

A:

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 distance between the parallel planes – 2x + y +z = 0 and 10r – 5y – 5z – 11 = 0. Note:…

A:

Q: coordinates

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Q: Find the distance between the point P(1, -2, -3) and the plane x + 2y + 2z - 15 = 0. Answer:

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Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

A:

Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: find the distance from the point to the plane. (3, 0, 10), 2x + 3y + z = 2

A: the given point is (3,0,10) the given equation of the plane is 2x+3y+z=2 we have to find the…

Q: .Find the value of x if H is the midpoint of GJ, GJ = 4x - 6, and GH = 27. %3D %3D

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

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Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.

Q: Evaluate the length of the curve y = 2 + Vx , 3 < y< 4

A:

Q: Find the point on the plane x – 3 y – 2 z = 14 that is closest to the point (0, 3, 3) .

A: We have the plane x-3y-2z=14 The normal vector to a plane ax+by+cz=d is a,b,c Hence, the normal…

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.