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

Q: write down the equation of the pair of straight lines joining the origin to the points of…

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

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

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Q: How would you create a parallel line that passes through a given point using rotation?

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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: We are supposed to find the distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t…

Q: Calculate the distance from the point P(9,4,3) to the line which contains points A(1,0,1) and…

A: we use  product rule to find distance between line and point

Q: Suppose the symmetric equations of lines l1 and l2 are = 2 – y = z and x = -1, 2 3 espectively.

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

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Q: find the nature of triangle formed by the lines x2-3y2=0 and X=2

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Q: find the nature of triangle formed by the lines x2- 3y2 =0 and X=2

A: Nature of triangle is isoscelene

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

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Q: What is the image of the point (4, -4) after the reflection over the line y = x-2?

A: we have to find the image under given line

Q: Find the exact value of the distance between the line of intersection of the planes 2x-y+2z 6,…

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Q: Find the equation of the line through point (3,7,-11) y is perpendicular to the xz-plane

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

A: Given query is to find the point where tangent line is horizontal.

Q: 1 What is the image of the point (-4,-2) after the reflection over the line y = - -X- 1?

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Q: Find nature of the triangle formed by the lines x2-3y2=0 and x=2

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Q: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is parallel to the line y…

A: Given curve is y=2x3-3x2-12x+20 Given line is y=2-12x=-12x+2  Slope of the given line is -12.…

Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: Consider point P(4, 2) and line l with equation −3x+4y=6 .

A: Substitute x=4 and y=2 into the given equation. -12+8=-4

Q: Use slopes to show that the square with vertices at (-2, 5), (4, 5), (4, -1), and (-2, -1) has…

A: Given that the four vertices of the square are: A4, 5 ,B-2, 5 ,C-2, -1 and D4, -1   If a line passes…

Q: (a) The curve with equation 2 y 3 + y2 - y 5   = x 4 -2x3  +x 2  has been likened to a bouncing…

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

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Q: What is the dual of the phrase “three collinear points and a fourth point not on the line of the…

A: Answer :  Dual of any phrase can be find by replacing the conjunction connective with disjunction…

Q: The plane that passes through the point (5,2,2) and is perpendicular to both x-5z=-24x-5z=-24 and…

A: The direction ratio of the normal vector to the plane x-5z=-24 or x+0y-5z=-24 is (1,0,-5) The…

Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: Find the equation of the Mane that contains the line 3X - 2:2 = - 39 = 7-7 and that is Para llel to…

A: When the plane is parallel to the line x-y+z=2: Here n1→=i^-j^+k^ and a→=2i^+3j^+k^ To find…

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

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Q: What is the image of (-2, –3) after a reflection over the line y = x?

A: Given : To determine the image of the point -2,-3 about y=x

Q: shows the image of (D2 • Ry-axis)(4, -3)?

A: D2∘Ry-axis4,-3 this means 4,-3will be reflected over the y-axis. And then it will be dilated by 2.…

Q: Find the curve in the xy-plane that passes through the point (4,8) and whose slope at each point is…

A: The curve in the xy-plane that passes through the point (4 , 8 ). Slope at each point is 3√x . We…

Q: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: What is the image of (0, -8) after a reflection over the line y = x?

A: The reflection of the point (x,y) over the line y=x is the point (y,x).

Q: Write down equation of the line in space passing through the points Po(1,0,0) and P (0, 1, 1).

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Q: What is the distance from the point S(-2, 3, -2) to the line of intersection of the planes 2x + 3y +…

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Q: Find an equation of a line containing the point (1, 7, -3) and parallel to the yz- plane.

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

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 9 which pass through the point (-7,…

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

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

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Suppose that L is a line through the points (a, 2, c) and (3, –4, 2) that is parallel to one of the…

A: Given that: L is a line passing through (a,2,c) and (3, -4, 2) and parallel to one of the axes.

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: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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

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Q: At point (1,y), what is y?

A: Note:- If two points is given in Cartesian form like  (2,5)  Then  x=2 and y=5 Means first one is…

Q: Find the orthogonal trajectory for the family of straight lines passing through (3,-5).

A: Find your answer below

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 :

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.