4. Find the distance between the two points S(-5,-2) and T(-3,4).

Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: Find the length of the curve over the given interval. r = 8, [0, π/6]

A:

Q: 15. Find the point on the line y 3x that is closest to the point (50,0).

A:

Q: C is the line segment from (4, 2) to (0, 0) followed by the line segment from (0, 0) to (-4, 2).…

A:

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

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

Q: Find the image of the line x = 1 under (a) flz) = z²

A:

Q: The line in R that is parallel to the y-axis and passes through the point (1, 2, 3) has equation + t…

A:

Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

A:

Q: 8) Find the distance from the point S(0,0,0) to the line through(-1,-1,2) parallel tov = 31 + k.

A: The given point S(0, 0, 0) The given line passes (-1, - 1, 2) parallel to v = 3i + k

Q: nded by the curve y2=4x and the lines x = 1 and x = 4.

A:

Q: - For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3-y = 1?

A:

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

A:

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: 2. Find the distance between and

A:

Q: Find the distance from the point S(1, 1, 5) to the line L: x = 1 + t, y = 3 – t, z = 2t.

A:

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

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: C is the line segment from (4, 2) to (0, 0) followed by the line segment from (0, 0) to (-4, 2).…

A:

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A: To find the points at which tangent line is horizontal , y' =0.

Q: 1. Find the point on the line y = x nearest to the point (4, 1).

A: Since, we have been asked to solve part(i) which aims to findthe point on the line y=x nearest to…

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: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: 4. The tangent of the acute angle between the lines y= 4x- 3 and y=x-5 is А. 5 В. C. 3 D. 5

A:

Q: Find the distance between the two given points. S (-1, 6) and T (-1, 14)

A: We know that distance between two point (x1,y1) and (x2,y2) is  (x2-x1)2+(y2-y1)2 Therefore distance…

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

A:

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

A:

Q: 2- The distance d from the point R=(1,4,-3) to the line L: x=2+t,y%3-1-t Z- 3t is 4.43 False True

A:

Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

A:

Q: Find the distance between lines x + 3y = 5 and x + 3y = 25.

A: The distance between two parallel lines can be calculated using the formula,

Q: 2. Find for x? +x+ y? +2 3xy the lines that are tangent and normal to the curve at point (3,2).

A:

Q: on the line ye -2x +8 that 1-) Find the point IS Close't to the onigin.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

A:

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: (1) ( ) Find the shortest distance between two lines given x +2 -8 y = and y 2

A:

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: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

A:

Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

A:

Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

A:

Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: 16. If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4. Find the…

A:

Q: A line that is normal to the curve x^2+3xy-4y^2=0 at (6,6) intersects the curve at what other point?

A:

Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

A:

Q: 3. Find the length of the curve y = x - In a, 1< x < 4.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 13. Determine the distance between the following lines. [x, y, z]= [4,5,9]+s[-3,4,-9] and [x, y, z]=…

A: Above question is solved.

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.