Find the coordinates of point L on the triangle below after a translation using the rule: (z, y) – > (z +6, y- 2) L'(1. -7) O L'-5, -5) O L'(-11, -3) O L1 7

Q: Find parametric equations for the normal line to the surfacez=-7x2 -9y2   at the point  (2,1,-37)

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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: Calculate the distance between the points J (-7,0) and L= (-2,-4) in the coordinate plane. Give an…

A: Given,            Two points J(-7,0) and L(-2,-4) in coordinate plane we need to calculate distance…

Q: Find the acute angle between the curves y = (/3)x3, and y = (/3)/5 x at the point of intersection…

A: The given curves are y=3 x3 and y=35x=15x and the point of intersection of the two curves are P1, 3.…

Q: 2)Passes point (1,3,7) and orthogonal to xy- plane.

A: The line which is orthogonal to x-y plane is lies on z-axis. Therefore the direction ratio's of the…

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: What are the new coordinates of the point (-5, 25) under the dilation (x, y) - (2x, 2y)? O (-10,…

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Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

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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: Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved…

A: Use the formula of arc length to determine its length. Now use to it determine the volume generated…

Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

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Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: Find the points that touch the x axis of curvev=u^2+pu+(n+1) Where n is your arid number for example…

A: Given that the curve in u,vthe axis is given by v=u2+pu+n+1 Given n=1147and let p =constant…

Q: distance

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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: Tangent drawn from the point (4, –3,10) to the intersection curve of z = x² and z = 25 – y² surfaces…

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Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…

A: we will use green theorem here to solve this question

Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: 1. Point K is located at (4. 2, 0. 3)and point Lis located at (5. 8, -0.6). What is the location of…

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Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

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Q: The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are…

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Q: Find the equation for the tangent plane to the surface x2 - 5xyz + y² = 7z2 at the point (-1, -1,…

A: Simplify the given equation of the surface in the form F(x,y,z)=0. x2-5xyz+y2=7z2x2-5xyz+y2-7z2=0…

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 passing through x1, y1, x2, y2, x3, y3 is given by,…

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: Find the lateral surface area of the cone generated by revolving the line segment 5x – 8y + 40 = 0,…

A: Detail solution written below

Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: Find the tangent plane to the equation z = 3x? – – 60) - y² – 4y at the point (4, 2, - -

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Q: ry = 10, z = 8, x = 9, y = 0, (i) about the z- and about the y-axis;

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Q: Find the lateral surface area of the cone generated by revolving the line segment 5x-8y+40=0 about…

A: Find lateral surface area.

Q: Find the tangent plane to the surface 8x2+y2+4z2 = 25 at the point ( 1, -1, 2 )

A: To find: The equation of the tangent plane at the point  1,-1,2. The given function for the surface…

Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

Q: find distance between plane(6x_2y_z+4=0)and point (3,2,1) P 3:08

A: Given,           The plane is 6x-2y-x+4=0 and the point is 3,2,1.

Q: Q1/: Find the distance between plane (6x - 2y - z +4 = 0) and point (3, 2, 1). (6 marks)

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Q: The distance between the point (7, 6, 9) and the plane 4x-3y-z+10=0 is units. (Round your answer…

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Q: What are the new coordinates of the point (-10, 10) under the dilation (x, y) (4x, 4y)? O (40, 40) O…

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Q: Va+ ド+で Find the distance between the point (0, 1,5) and the plane 3r + by – 2z-5 0.

A: topic - distance of point from plane

Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: Find a parameterization for a circle of radius 4 with center (-3,-1,2) in a plane parallel to the xz…

A: Aim: To find the parametric equation for the circle of radius with radius 4 and center -3, -1, 2…

Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3)…

Q: intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when…

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Q: The 50 g bullet travelling at 100 ms-1 strikes the 2 kg block centrally and is embedded within it.…

A: Please check step 2 for the solution.

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: 8. y- -x+4 , x=0, y=o, about the (x 20) y axis

A: y=-x2+4 and x≥0 ,x=0,y=0 about y axis

Q: What are the new coordinates of the point (3, -4) under the dilation (x, y) (0.25x, 0.25y)? O (3,…

A: We have to find the new coordinates of the point (3,-4) under the dilation (x, y) ----> (0.25x,…

Q: Find the length of curve along y = x² from (0,0) into (2,4).

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Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: Given that, the cone is generated by revolving the line segment  y = 53x,  0≤x≤4, about x-axis.

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.