The graph of y = x' is called a semicubical parabola and is shown in the accompanying figure. Determine the constant b so that the line y -x + b meets this graph orthogonally. Y y? = x y = -jr + b = -3*

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

Q: Find the equation of the plane with the given description. Passes through (6, 1, 5) and is parallel…

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Q: Find the distance from the point (-5, -1, -3) to the plane 5x + 3y + 2z = 1

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Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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Q: Find the distance between the point (1, 0, 2) and the plane 2x – 3y + 6z = 6.

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Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

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Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

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Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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Q: Find the distance from the point (−3,0,2) to the plane - 3x + y + 5z = 0

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Q: Find an equation of the plane that passes through the point (1,-1,1) and contains the line of…

A: Let P=(1,-1,1) and n1=<1,1,-1> ,n2=<2,-1,3> The vector a for the line of intersection,…

Q: Find the distance from the point (2, 2, 3) to the plane 2x + 3y + 5z = 0.

A: Formula of distance of a point from a plane:

Q: Find the distance from the point (-1, 3, -1) to the plane -1x + 2y -5z=1.

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: Find the general equation of the plane spanned by

A: Given vectors are 111 and 321

Q: 5. Find the exact value of distance from the point (1, -3, -1) to the plane 2x-y+3z = -5

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Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: Find an equation of the plane through the given point and parallel to the given plane. origin 2x -…

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Q: find the distance from the point to the plane. (0, 0, 0), 3x + 2y + 6z = 6

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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: Find an equation of the plane that is parallel to the y-z plane and that passes through the point…

A: NOTE: Refresh your page if you can't see any equations. . the equation of any plane parallel to the…

Q: Find the equation of the plane that contains the point (4, 0, −2) and is perpendicular to the planes…

A: The equation of the plane passing through the point x0, y0, z0 is given as…

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

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Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

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Q: Find the general form of the equation of the plane with the given characteristics. Passes through…

A: The plane, let P1, whose equation is required is perpendicular to the plane, And passes through the…

Q: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: Find the distance from the point (1, -4, 4) to the plane −2x−4y+3z=5

A: Given:The point (1, –4,4) and the equation of the plane –2x–4y+3z=5.The distance from the point…

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

A: Given,             Point  (3, 1, −2)          Plane   x + 2y − 2z = 4

Q: Find the distance from the point (5, -4, 1) to the plane −3x−2y−3z=−4

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Q: Find an equation of the plane. The plane through the point  (8, −3, −3)  and parallel to the plane…

A: We know that two parallel planes have same direction ratios(i.e. the coefficients of x,y and z…

Q: 4. Determine the equation of the plane passing through the point (1, –4, 3) and parallel to x – y…

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Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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Q: Find the distance of the point (3,8,2) from the line x-1 -y+3 -z+2 measured -3 2 -4 parallel to the…

A: Given point 3, 8, 2Given line - x-12=-y+3-4=-z+2-3Let the parameters be equal to an arbitrary…

Q: Find the distance of the point (3,8,2) from the line =22= measured parallel to the plane 3x + 2y- 2z…

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Q: Find the distance between the point (3, -4, 2) and the plane 5x- 2y +z = 10.

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Q: Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane…

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Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

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Q: Find an equation of the plane. The plane through the point (7, –2, –8) and parallel to the plane 6x…

A: We will solve the following.

Q: Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane…

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Q: 3. Find the equation of the plane parallel to the plane with equation 18x + 6y – 5z = 0 and passing…

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Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…

Q: Find the distance between the point (1, 0, 2) and the plane 2x − 3y + 6z = 6.

A: To find the distance

Q: Find the distance from the point B = (1,0, 2) to the plane 2P whose general equation isx + y - z =…

A: Given: equation of plane is x+y-z=1  We know that distanced from the pointx1,y1,z1 to the…

Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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