Show that the locus of the point whose distance from Y-axis is thrice it's distance from (1,2,-1) is 8x2 +9y2+8z2+18x-36y+18z+54=0

Q: An ant is walking on the xy-plane is such a way that its distance to the point (2, 4) is always the…

A: Solution: Let the point P(x,y) is the position of Ant and given that the distance from P(x,y) to…

Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on this…

A: We answer only one question at a time , so we will answer the first question since the exact one…

Q: Find the equation of locus of a point which is at a distance 5 from A (4, -3).

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Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: Find the point on y – axis which is equidistant from the points (3, 1, 2) and (5, 5, 2)

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Q: Two planes with equations x - y + 2z=4 and x + 2y - z = -5 intersect along a line L. Determine the…

A: Find the intersecting line L. For any random point on the line L, we can find the general distance.…

Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: In the coordinate plane, right triangle AXYZ is reflected over the line y = x. 5 3 X 2- -6 -5 -4 -3…

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Q: Find the point on the line 6x + y = 6 that is closest to the point (-4, 1). (x, y) = %3D

A: We have to find a point on the line 6x + y = 6 that is closest to the point (-4,1). Concept Used -…

Q: Find a plane containing the point (-4,-4,6) and the line of intersection of the planes -x + 3y – 2z…

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Q: 11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

A: This question is related to coordinate geometry, We will solve it using given information.

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: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: Through any point (x, y) of a certain curve which passes through the origin. lines are dawn parallel…

A: Draw the sketch of two possible cases of the given problem:

Q: 11) The distance from the point S(7, 6, -8) to the line x = −2 + 4t, y = -9 + 3t, z = 3 + 12t 12)…

A: #11) Given: Point = S7, 6, -8 and the line x=-2+4t, y=-9+3t, z=3+12t. To find: We have to find the…

Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

Q: I am on a question that asks to find the distance from a point, (4,-2,6), to the xy-plane. I was…

A: topic- distance between point and plane distance of a point from xy plane  is the z coordinate of a…

Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: 7. Find the distance between the point (- 3, 2, 1) and the plane with equation x - 2y + 3z = 5

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Q: The plane containing the point (0,7,-2) and parallel to the plane -x + 8y + 6z = Ax+By+Cz = D. 4 has…

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Q: What are the new coordinates of the point (-14, -24) under the dilation (x, y) → (0.5x, 0.5y)? O…

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Q: 3. Line segment JK in the xy-coordinate plane has endpoints with coordinates (-4, 11) and (8, -1).…

A: As per guidelines we can answer only one question at a time, so the first question can be answered…

Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

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Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: The distance between the points (1,−2, 0) and (4, 0, 5) is _____ .

A: Given Two points; (1,−2, 0) and (4, 0, 5)

Q: Find the number of points in the xy-plane with integer coordinates located at a distance 5 from the…

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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 distance from the point K(3, -2, 0) to the xy-plane is Select one: 3 -2

A: Find out the correct option.

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

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Q: A point moves such that the ratio of its distances from two fixed point is constant, show that its…

A: Let the moving point be P (x, y, z). Let A(a, 0, 0) and B(-a, 0, 0) be two fixed points.

Q: 3. Through the point (4, -5, 20) and perpendicular to the plane x + 3y – 6z - 8 = 0.

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Q: Find equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

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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: Choose the correct option. If the locus of the circumcentre of variable triangle having sides x = 0…

A: From the given information Coordinates of A is (0,2) At B , the value of y is 2…

Q: What are the new coordinates of the point (-14, -24) under the dilation (x, y) (0.5x, 0.5y)? O (-7,…

A: Given coordinate of point ( -14 , -24 ). dilation is , ( x , y )→ ( 0.5x , 0.5y )

Q: 5. Parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,-4) over the line y = x ty 6.…

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Q: Find an equation for the set of all points (r, y, z) equidistant from point 10.) (1,0, 2) and the…

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Q: X ▪ Find equation of plane which is contains line L: 3y-2 2-7 = -3 -1 and parallel to intersection…

A: We will find a point vector on the plane a→ and normal vector to the plane n→ then equation of plane…

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: The 3 lines x = 3, y – 2.5 = --(x – 0.5), and y – 2.5 = x – 3.5 intersect at point P. Find the…

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Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: Find the distance of the point (2, 6, 4)  from the x-axis by two methods

A: To find the distance between the point.

Q: 6. Find the distance between the point (-3, 1) and the line 4x + 3y + 4 = 0.

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Q: If a point moves on a plane is such a way that the sum of its distances from two fixed points on the…

A: Let, x,y be a point on the locus.p,q and r,s be two points.distance between x,y and p,q…

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: The distance from the point S(-7, 8, -4) to the plane 10x+2y+11z=2. 20 3 8 15 8 225

A: The equation of the plane is  10x+2y+11z = 2 The point is S-7,8,-4 To evaluate : The distance from…