Question 2: The locus of mid points of the perpendiculars drawn from points on the line x = 2y to the line x = y is: (а) 2х - Зу %3D0 (b) 3х - 2у %3D 0 (c) 5x - 7y = 0 (а) 7х - 5у %3D0

Q: A line passing through (0, –3) and is perpendicular to y =;x – 4. х —

A: The given line passing through the point 0,-3 and it perpendicular to the line y=52x-4. Calculation:…

Q: What are the directing cosines of the line whose symmetric is (x + 2)/ - 1= (y-3)/ 2 = (z + 4)/ 6

A:

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

A: Solution is done in step 2

Q: 4. Find the equation of the locus of the points P(x, y) whose distances from the point (3,2) are…

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Q: The pair of lines defined by the equations y =- 3x +1 and y =-x+1 are O parallel to each other. O…

A:

Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

A:

Q: Find parametric equation of the line segment ( L1 ) between the points P(1, 8, 9) and Q(5, 9, 18).…

A: To find the angle between two lines

Q: Show that the locus of the point whose distance from y-axis is thrice it's distance from (1,2,-1) is…

A: The equation of the ellipse is 8x2+9y2+8z2+18x-36y+18z+54=0 The locus of the point whose distance…

Q: If the lines joining origin to the points of intersection of the line fx - gy = 2 and the curve x²…

A: Though it is analytical geometry problem but it is a B.SC problem, more than high secondary…

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: 11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

A: This question is related to coordinate geometry, We will solve it using given information.

Q: 5. Find the exact value of distance from the point (1, -3, -1) to the plane 2x-y+3z = -5

A:

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

Q: Give the equation of the line passing through the point (– 3, – 9) that is parallel to y =

A: We will find the equation of the line.

Q: Find the equation of the line in standard form (i.e., y = mx + b) that conatins the point (-3,5) and…

A: We have to find the equation of line in standard form if it is passing through the point -3, 5 and…

Q: If the line through the point (3.-4,-1) and parallel to the vector i+j+k. The equation of the line…

A:

Q: What is an equation of the line that passes through the point (–6, –6) and is paralle to the line x…

A:

Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

A:

Q: 15. Reflect the point (2, -4) over the y- axis. O a) (-4, 2) O b) (-2, 4) O c) (-2, -4) O d) (2, 4)

A: We know that the reflection of a point about the y-axis makes the x-coordinate negative. So, the…

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: If line r has the equation y = - 2 what is the equation of line r given that line rwas dilated by a…

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Q: d the eqation of the line that passes through A(1,2,1) and intersects the line x+1 у-2 z+1 %3D at…

A: Topic:- geometry

Q: The diagonals of rhombus LMAO intersect at P(4, 11). If the equation of the line contains diagonal…

A:

Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

A:

Q: Line 1: 3 x=³_12Y=z-8 2 4 Line 2: x=-2t y=2+2t z=6+2t 1. If the given lines intersect at a point,…

A: Given lines: Line 1: x-34=1-y2=z-8 Line 2: x=-2t, y=2+2t, z=6+2t The objective is to find the angle…

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

A:

Q: The plane with equation = (6,-2,3)+a(1,3,0) + b(2,2,-1) intersects the y- and z- axes at the points…

A: Vector equation of line is r'→=a→+αb→-a→where, a→ is the position vector of the point A.…

Q: Suppose a line is given parametrically by the equation L(t) = (5,-5,-3t,3t). What vector and point…

A:

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A:

Q: The coordinates of a point on the line x+ y+1 = 0 which is at a distance /2 units from the line 3x +…

A: Given: The line x+y+1=0 which is at a distance 2 units from the line 3x+4y-2=0 To find: Coordinates…

Q: Region A is formed by bounding the lines y= T, y = 6, and the y-axis. Determine which pair %3D of…

A: Region A is formed by bounding the lines y=x, y=6 and y-axis. We have to determine which pair of…

Q: Find equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

A:

Q: Find general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

A:

Q: 5. Parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,-4) over the line y = x ty 6.…

A:

Q: 9. Reflect the point (3, 2) over the following axes or lines. Reflection Over New Coordinates x -…

A: Definition used -                    Reflection of a point over the x-axis -…

Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: Suppose ABC is reflected across the line x = -1. What are the coordinates for the image of A?

A: There is no change in y coordinates while taking mirror image across x = k.

Q: 3. The equation showing a family of lines passing through the point (1, -1) is given by * у%3D тх —…

A: Given a point(1,-1). We need to find the equation of  a line passing through the given point.

Q: If point A is reflected over the y-axis and its original location was (2,3), where is its new…

A:

Q: Find the distance of the point (3,8,2) from the line =22= measured parallel to the plane 3x + 2y- 2z…

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Q: Find an equation for line that passes through point p(8,6) and perpendicular to v=2i+3j

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Q: Q1/The line joining origin and point of inter section of the lines (x = 1 + 2t, y = -3 + 4t, z %3D =…

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Q: standard form of the line with center (5,1) and tangent to the line 7x+2y=17

A: Given Data: Center: (x1, y1) = (5, 1) Tangent: 7x+2y=17   The general equation of tangent is,…

Q: Show that the locus of the point whose distance from Y-axis is thrice it's distance from (1,2,-1) is…

A:

Q: 1. The midpoint of points A and B is given to be (-,–1). Suppose two lines l1 and lz are…

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Q: Find an equation of the line normal to the plane containing the line I-2 y+1 %3D and +1 - y+8 %3D 3…

A: The given problem is to find the equation of line normal to plane containing the lines at their…

Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3- 2t ,y=-2t+1,z=t is

A: Distance between two Parallel Lines we calculate as a distance between intersection of the lines and…

Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0.

A: Introduction :