Find the distance from the point (1,–4,2) to the line x=2+t, y =-2+2t, z = 4 –t Try not to use any formula

Q: Find the distance between the point (5, 1) and the line y = 3x + 1. O 3V10 O 7/10 O 9/10 O 5V10

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Q: Find the point on the line y=x that is closest to the point (3, -1)    The point is (___ , ____)

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Q: Qz find the alistance from the Point to the line (zy-) , メーマty4zt?2t

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Q: Find the distance from the point s(1,-6,2)to the line x = 2 + 3t, y = -4 + t,z = –2t Ans >>d=1.79

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Q: 4. The midpoint of the line segment with endpoints (x1, yı) and (x2, y2) is given by the formula

A: we know, the midpoint of the line segment with end points (x1,y1) and (x2,y2) is given by the…

Q: Find the shortest distance from the point x = (-3, 0, -12)  to the line r = t(0, -2, -2).

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Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Perpendicular to the line y=−1/2x+1 containing the point (3,6)

A: Solution is done in step 2

Q: Find the length of the curve. 33 X = x=11t°, y= ², t,0stsv3

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Q: Find the exact length of the curve. x- 2, y =? - 2, Osts9

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Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

Q: Find the distance between the point (-3, 1, 5) and the line given by x = 5+t, y = 1- 2t, and z = 3-…

A: Given : Point A ( -3,1,5) x = 5+t  y=1-2t  z=3-t

Q: Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

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Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

Q: Find the length of the curve. 29) y = 1,3. 6. 1. from x = 1 to x = 3 2х

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Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

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Q: Find the distance from the point (1,1,5) to the line x=1+t, y= 3-t, z=2t O 2.236 O 0.36 O 36

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Q: The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y.

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Q: The distance from a point (2, y) to a line x – 2y + 3 = 0 equal to v5. Find the value of

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Q: Find the distance from the point S= (1, 2, 1) to the line x = 2-t, y=-1+2t, and z=2+ 2t.

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Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

Q: Find the length of the curve.  y = (9 - x^2/3)^3/2 from x = 1 to x = 27

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Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. O (5)^0.5 O 7 O 2(3)^0.5 O…

A: Given: Equation of line is: X = 1+ t Y = 3 - t Z = 2t To find: distance from the point (1, 1, 5) to…

Q: Find the length of the curve y=x^3/2 from (1,1) to (2,2squareroot2)

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Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: Find the distance from the point P(-1,2,4) to the line given by x=2t y=1+t z=3t

A: Given query is to find the the distance between point and the line

Q: Find the shortest distance from the point (- 1, – 2, 5) to the cone z = x² + y². Please | round to…

A: Distance of a point from cone is                                      d=(x-x1)2+(y-y1)2+(z-z1)2 from…

Q: Find the length of the curve x = 3t2 + 10, y=2t3+ 11, O<t<1.

A: Given,         The length of the curve x=3t2+10 , y=2t3+11 , 0≤t≤1We know that,         The length…

Q: Q1/ Find the equation of the circle tangent at least to three lines (y = 1, y 5, x 2 and x = 7). %3D

A: We have considered the first 3 lines as the line of the tangents For more see below

Q: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

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Q: Find the distance from the point (4, 4, 3) to the line x=0 ,y=4+t ,z=3+4t

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Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

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Q: Find the distance from the point to the line. Knowing that the point Po (2, 1, 3), x= 2+2t, y= 1+6t…

A: This question is based on distance between point and line in 3d geometry.

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

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Q: Find the length of the curve y x7 from ¤ = 0 to x = 15. 2/3

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Q: Find the point P on the line y=3x that is closest to the point (40,0). What is the least distance…

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Q: Find the approx. distance of the point (6, -3) from the line 2x – y +4 = 0 a. 6.5 units O b. 10.5…

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Q: Find a distance from the point S(1,1,5) to the line x=1+t, y=3-t,and z= 2t

A: We need to find the distance of the point (1,1,5) and the given line.

Q: Find the length of the curve. y= x? + from x = 1 to x = 5

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. *

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Q: Find the length of the curve x = et - t, y = 4et/2, -8 ≤ t ≤ 3.

A: Consider the following: Given parametric equations are: x=et−ty=4et2−8≤t≤3

Q: Find the distance from the point (0,0, 0) to the line a = 5 + 3t, y = 5+ 4t, z =-3 - 5t. Lütfen…

A: Definition used -              If we have a parametric equation of a line-…

Q: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

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Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: Determine the exact distance from the point P (1,2) to the line (-1,3) + t(2,9), t e R . Show your…

A: Given

Q: Q2: Find the distance from the point R( 2,2,10) to the line: x=t y=1+t z = 3-t

A: Here first we select a general point on the line Now, we find the direction vector of that point to…

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.