Let a rectangular a'y'z'-coordinate system be obtained by rotating a rectangular xyz-coordinate system counterclockwise about the z-axis (looking down the positive z-axis) through the angle 0 . Find the 4 %3D x'y'z'-coordinates of the point whose xyz-coordinates are (0,3,0). = Z || ||

Q: The intersections with the abscissa axis of the image function are: f (x) = x2 + 10x + 21

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Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: What kind of transformation results in applying the rule (x, y) → (x – 5, y) in the coordinate…

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Q: If a half-turn centered at F(3,7) is applied to the point A(9,12), what are the coordinates of its…

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Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Find Vƒ(P) and D7f(P). (a) f(r, y, 2) = yf + z² – 4xz; Ū = } i – $ j+ k; P(-2,1,3)

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Q: If the xy-coordinate axes are rotated , find the XY-coordinates of the point (x,y) = (4,5

A: The new coordinates (X, Y) of a point (x, y) can be found using the following rotation…

Q: Find the points on the graph of z = xy +8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

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Q: Find an equation of the povalbola in standovet form focus at F(-4,0) and divectrix ;X=-4

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Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

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Q: Find an equation for the contour of f(x, y) = 2a²y + 6x + 15 that goes through the point (4, 1).…

A: A contour line of the quadric surface is the curve of intersection of the quadric surface with the…

Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: Plot z = sin(r)/r with r = Væ2 + y?, -8 < x < 8, -8 < y < 8.

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Q: Let u=. (a) Graph u in the coordinate plane, with initial point (0, 0).   (b) Find the length and…

A: (a) A vector u is represented in the plane with initial point Px1,y1 and terminal point Qx2,y2.…

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: T/f Two parallel lines in the 2d plane never intersect each other

A: Given that two parallel lines in the 2D plane never intersect each other. Here we have to determine…

Q: orthogonal curves of the curves xy=C graph

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Q: If the temperature at the point (x, y, z) is given by T (x, y, 2) = 70 + Se(x² +y}, find the…

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Q: Q5/A// Find the distance between the point P =(2, 1, 1) and line L:x = -2+ 5t, y= 2 +4t, z = -3-6t.…

A: Use distance formula

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.