Question: By using normals, analyze the geometric relationship of the systems of equations. Determine the intersection of the planes, if it exists. If the intersection is a line, express your answer in parametric form.  a) P₁ : 2x + y + z = 6      P₂ : x - y - z = -9     P₃ : 3x + y = 2 [One POI (-1,5,3)] b) P₁ : 2x - y + 2z = 2      P₂ : 3x + y - z = 1      P₃ : x - 3y + 5z = 4 [Show Co-planar-Triangular Prism] c) P₁ : 2x + y - z = 0     P₂ : x - 2y + 3z = 0     P₃ : 9x + 2y = 0 [Intersects at Line-State Line]

Q: A line passes through the center of a circle and intersects it at points (-1,2) and (5,10). What is…

A: equation of line passing through points (x1, y1) and (x2, y2) is:  y-y1=y2-y1x2-x1(x-x1)    Equation…

Q: I need help with solving the equation. I am not where i am making the error but i keep getting the…

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Q: The given points are (4,2,2), (2,6,2) and (0,2,6). Find the general equation of the plane. Solve in…

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Q: 3) What is the center of the circle represented by this equation? (x - 7)2 + (y + 4)2 = 9 A) (4, 9)…

A: The equation of the circle is  ( x - h)2 + ( y - k )2 = a2 Centre is ( h ,k ) and a = radius  ( x -7…

Q: 6. The z-axis. Answer:

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Q: Determine whether the graph of the given equation is symmetric with respect to the x-axis, the…

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Q: (x + 4)2. (v- 1)² 1? 36 What are the lengths of the major and minor axes of 16 A Major: 36; Minor:…

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Q: The center of the circle (x+3)2+(y-2)2=13 is(3,-2)

A: The given circle equation is (x+3)2+(y-2)2=13

Q: Find the distance from (-5,9, –12) to each of the following: 1. The xy-plane. Answer:

A: Given point :-  (-5,9,-12) To find:- Distance of given point to plane xy

Q: Find the distance from (-5, 9, -12) to each of the following: 1. The xy-plane. Answer: 2. The…

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Q: ketch the surface

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Q: Find an equation of the plane passing through the points (1, -2,3), (4,5,-6), and (7,8, -3).

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Q: In the Cartesian plane below, the map of two perpendicular cross country skiing trails is shown that…

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Q: Why doesn't this figure have vertical line symmetry

A: figure does not have vertical symmetry

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.