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

Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

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: What is the y-coordinate of any point in the xz-plane?

A:

Q: Find an equation for the set of points equidistant from the a. xy-plane and yz-plane. b. x-axis and…

A: a) Let (x,y,z) be such point that xy-plane and yz-plane are equidistant from it.Distance of (x,y,z)…

Q: Find the point on the plane 5x+3y+: =11 that is nearest the origin. What are the values of x, y, and…

A: Given: The equation of plane 5x+3y+z=11, To determine: The point on the plane that is nearest the…

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A:

Q: draw the plane given by the equation  x + y + z = 0

A: x+y+z=0 It is a plane passing through origin.

Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

A:

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A:

Q: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1 and…

A:

Q: Sherry is drawing a map of her workplace and her usual lunch meeting place on a standard (æ, y)…

A:

Q: Find the equation of the plane through the point (2, –1, –5) and containing the line | x = 3 – 2t, y…

A: We have to find the equation of the plane, passing through the point (2,-1,-5) and containing the…

Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

A:

Q: Find the general equation of the plane that contains the point (2,0, 3) and the line r -1+t, y =t, z…

A:

Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

A:

Q: y =(+ + +)* x = 4t + 1, 4

A:

Q: 4. Write the equation of the plane parallel to the z-axis, with xy-trace x + y - 2 = 0.

A: Write the equation of the plane parallel to z axis, with xy trace x+y-2=0.

Q: Determine the scaler equation of the plane with × -intercept=2, y intercept=-1 and z intercept=3

A:

Q: Draw the plane given by the equation. x + y + z = 4

A: x+ y+ z= 4

Q: ) Eliminate the parameter t to find a Cartesian equation for: x = t² and y = 3 + 5t. and express…

A:

Q: Sketch the plane defined by the equation T1:2x – 5y – 10 = 0.

A:

Q: Find an equation of the plane. The plane through the point (4, 0, 2) and perpendicular to the line x…

A: To find- Find an equation of the plane. The plane through the point 4, 0, 2 and perpendicular to the…

Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Given curves are y=2x,y=4x,y=3-x & y=15x. We know that curve y=mx is equation of straight line…

Q: Show that the curve a(t) = (t, , ) lies in a plane and find the equation of this plane.

A: For all 't' , we have α'(t) = 1 , -1t2 ,-1 - 1t2α"(t) = 0 , 2t3 , 2t3 Now  α'(t) × α"(t) = 2t3 ,…

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 point in which the line meets the plane x = -1 + 3t, y = -2, z = 5t; 2x - 3z = 7

A:

Q: Find the point at which the line 7(t) = +t intersects the yz plane.

A:

Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve. x = t2,    y = t5

A: A curve is a two-dimensional object with equation of the form y=f(x). Curves can be parameterized to…

Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

A:

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2). O…

A:

Q: How far trom the y-axis is the center of the curve 2x? + 2y? + 10x - 6y - 55 = 0? O 2.50 O 2.75 O…

A:

Q: Show that the plane whose intercepts with the coordinates axis are x = a, y =b, z c has equation :…

A: Consider an equation of plane as It is given that the intercepts of plane are x=a,y=b and z=c. So,…

Q: :: Find the y-coordinate of the point on the plane x+ 6y + 7z = 3 that is closest to the point (-14,…

A:

Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: Find the point at which the line 7(t) +t intersects the | xz plane.

A:

Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: Find an equation for the set of all points equidistant from the planes y = 3 and y =-1.

A: Find an equation for the set of all points equidistant from the planes y = 3 and y = -1.

Q: find the point in which the line meets the plane x = 2, y = 3 + 2t, z = -2 - 2t; 6x + 3y - 4z = -12

A: The equation of plane is 6x + 3y - 4z = -12. The coordinates of the line is x = 2, y = 3 + 2t, z =…

Q: Find the equation of the plane that contains the point P(-6, 5, 7) and is perpendicular to the line…

A: Use direction ratios of line to find direction ratios of plane. Then use the point to find equation.…

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…

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.