A piece of a broken plate was dug up in a archaeological site. it was put on top of a grid with the arc of the plane passing through A (7,0 ) ,B(1,4) and C (7,2) .Find its center and the standard equation of the circle describing the boundary of the plate

Q: Find the direction cosines of the line passing through the two points (-2,4,-5) and (1,2,3). Find…

A: We know that direction cosines of line passing through two points Ax1, y1, z1, Bx2, y2, z2 is given…

Q: Find the equation for the plane through the points Po(1,-5, - 3), Qo(-1,1,-2), and Ro(-4,4,2). Using…

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Q: Find the equation for the plane through the points Po(-2, - 4,2), Qo(5,5,4), and Ro(5,2,3). Using a…

A: Basic algebraic equations are to be solved

Q: What is the equation of the circle with center (-1,-2) and passes through the point (6, 4)?…

A:

Q: Find an equation for the plane through the points (3, 4, 33), (2,1 -2), (0, 1, –1). The plane is

A:

Q: Find parametric equations for the line that passes through the points P(-3,7,9) and Q(4, 1, -5).

A: The given points are P-3,7,9 and Q4,1,-5. The line containing the point x0,y0,z0 and parallel to the…

Q: Find the equation for the plane through the points Po(3, - 5, -5), Qo(-4,- 2,0), and Ro(1, - 2, -…

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Q: How do we prove that a shape is a parallelogram using coordinate geometry?

A: We will use the properties of parallelogram to prove this.

Q: A bridge is built in the shape of a semielliptical arch. The bridge has a span of 140 feet and a…

A: equation of the ellipse is x2/a2 + y2/b2 = 1

Q: Find the equation for the plane through the points Po(3,4,2), Q,(-1,0, – 1), and R,(-1,-3,0). Using…

A: we have to find the equation of a plane passing through the points P0(3,4,2),Q0(-1,0,-1) and…

Q: Find the equation for the plane through the points Po(1, – 5, – 3), Qo(-3, – 5, – 1), and Ro(-…

A: -5x+4y-10z=5

Q: Find the center and radius of the circle whose diameter has an endpoint at (3, -4) and the origin. 5…

A: Given that the endpoints of the diameter are 3,-4 and 0,0.

Q: Find the distance from the point to the plane. (2,5,6), у + 6z%30 The distance is

A:

Q: Find the equation of a plane bisecting the line segment joining (2,0,6) and (6,2,4) and…

A:

Q: Find an equation of the plane pirpendicular to the line through (2,2,-4) and (9, "1, 3) and…

A:

Q: Determine the general form of the equation of the circle whose center is (3,2) and whose graph…

A: Given:Center3,2Point1,2Formula:x-a2+y-b2=r2

Q: Determine if the line 8x-y= 2 and the line containing the two points (1,3) and (2,-4) are parallel,…

A:

Q: Center: (−4, 5); Radius: 2.Write the standard form of the equation of the circle with the given…

A: Given,Center :(-4,5)Radius : 2

Q: Point O(-2,3) is the center of the circle that passes through the origin of the coordinate system.…

A:

Q: Find an equation of the plane. The plane through the origin and the points (2, -3, 5) and (5, 3, 1)

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Q: Find an equation of the plane. The plane through the point (5, -3, -3) and parallel to the plane 4x…

A: We can use the concept of plane in order to solve the given problem.

Q: Find the equation for the plane through the points Po(-3,- 2, – 4), Qo(2,1,3), and Ro(3, - 2, – 5).…

A:

Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Find equations for the line of…

A: Given equation of planes - 3x+6z = 1                ........................(1)2x+2y-z = 3…

Q: Find the equation of a circle who Center is at (3,-6) and radius 4.

A: Center = ( h,k ) = ( 3,-6 )  Radius = r = 4

Q: the equation of the circle with center (−5,−7) that p

A: Here the center of the circle is (-5,-7) and  passing through the point (7,5)

Q: 6) Find the distance between the point (1, -4, -3) and the plane 2x – 3y + 6z = - 1.

A:

Q: 4. Calculate the distance between the point Q(3, 1, 7) and the plane 2x-6y-z=3. Don't use a formula.…

A: Given point Q(3,1,7)and the plane 2x-6y-z=3. The objective is to find the distance between the point…

Q: Find the equation for the plane through the points Po(0,5,3), Qo(5, – 3,5), and Ro(2,1,5). Using a…

A:

Q: Find the distance from the point (-5, –13,6) to the plane –9x + 3y – 8z = -67. Distance is ...

A: Given:            point a(-5,-13,6)=(x0,y0,z0)            plane equation is -9x+3y-8z+67=0we know…

Q: Find the equation for the plane through the points Po(2, – 4,4), Qo(0, – 2, – 3), and Ro(- 4,5,4).…

A: Given: P0(2, -4, 4), Q0(0, -2, -3) and R0(-4, 5, 4).

Q: A line passes through the center of a circle and intersects it at points (2,3) and (8,7).What is the…

A: A line passes through the center of a circle and intersects it at points (2,3) and (8,7).What is the…

Q: Find the parametric and symmetric equations for a line that passed through the points (2,0,8) and…

A: Representing the points as the points vectors we get,  2,0,8 and -2,6,4 The direction numbers are…

Q: 4. Find the equation and sketch the graph of a plane that is parallel to the yz-coordinate plane and…

A: We know that equation of plane parallel to yz-coordinate plane is given by: x=k where k is some…

Q: Give an equation of the plane: (a) (2 points) that contains the point (-2, 1, –3) and perpendicular…

A: GIVEN the plane that contains the points (-2,1,-3) and perpendicular to a line which is passing…

Q: Equation of the circle with center (-4, 9) and radius 8 is

A:

Q: Find the equation for the plane through the points Po (0, – 5,5), Qo(- 4,0, –- 2), and Ro(- 2,0, –…

A:

Q: Find an equation for the plane through the points (5, 3, 5), (2, 2,0), (1, 0, -2). The plane is

A: We have to find the equation of plane

Q: Find an equation of the circle that satisfies the given conditions. center (8, 7), graph tangent to…

A: Given, center (8, 7), graph tangent to the x−axis

Q: Point P (0,2) is the point of intersection of y axis and perpendicular bisector of line segment…

A:

Q: Find an equation of the circle that passes through (1,1) & its center is the midpoint of (3,6) &…

A:

Q: (1 point) Find the point at which the line (-2, 1, –5) + t(-1,–1, –2) intersects the plane 4x – 2y +…

A: To findcthe point at which the line (-2,1,-5)+t(-1,-1,2) intersects the plane 4x-2y+2z=-68

Q: A cell phone tower is located at (5,-2) on a coordinate plane with units in kilometers. What is the…

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Q: Find the equation of the circle with center (9,2) and passes through the point (12,-2)

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Q: 5) The point (-1,2) is on a circle whose center is (2,6). What the standard equation of this circle?

A:

Q: Find the equation for the plane through the points Po(0, – 3, – 5), Qo (3, – 3, – 1), and Ro(5,2,0).…

A:

Q: Find an equation of the plane through the point (-2, -1, 3) and parallel to the plane 3x+3y+5z=03.…

A:

Q: 15. In the xy-plane, (-3, 1) and (4, 3) are the endpoints of a diameter of a circle. What are the…

A: Endpoints of diameter are (-3, 1) and (4, 3).

Q: Find its center, and the standard equation of the circle

A: Consider the general equation of a circle with center (h, k) and radius 'r', x-h2+y-k2=r2 A point on…

Q: Find the equation for the plane through the points Po(4, - 3, - 5), Qo(-4, - 3,4), and Ro(- 1,1,5).…

A: Mi

Q: Find the equation of the circle with points (-1,9) and (5,3) as the end points of a diameter

A:

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.