Find the equations of planes that just touch the sphere (x – 4)² + (y – 5)² + (z – 2)² = 16 and are parallel to - - (a) The xy-plane: and (b) The yz-plane: and (c) The xz-plane: and
Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…
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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: fficients of x, y, and z in the given equation of the plane. ..... z= -7+ 9t. pe expressions using t…
A: Find parametric equation.
Q: 2. The plane containing the point (-8, 3, 7) and parallel to the plane given by 4x+8y-2z=45.
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Q: Find parametric equations for the line of intersection of the planes x + 2y + 3z = 4 and 5x + 6y +…
A: Given: x+2y+3z=4 and 5x+6y+7z=8To obtain the parrametric…
Q: Find the standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…
A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…
Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.
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Q: Find the standard equation of the sphere with center (-4, 3, 8) that is tangent to the plane given…
A: The center of the sphere is (-4,3,8) . The tangent plane is 3x+8y-4z=24 The radius of the sphere is…
Q: Determine the equation of the plane containing the points (3, 1, 4) and (2,7, 1) and is perpen-…
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Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…
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Q: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…
A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…
Q: 5z' + 3z gral z² - 4 plane, is
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Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.
A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…
Q: Find the general equation of the plane spanned by
A: Given vectors are 111 and 321
Q: Find all point cs) 2= 8- 3x2- 2y2 マh where the fameyent plane orlhugana l i's to とk 2ihe. X 2-31,…
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Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…
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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: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…
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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…
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Q: 3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the…
A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…
Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…
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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 the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…
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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: Find an equation for the plane through the point (3, 4, −4) and parallel to the plane defined by 4x…
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Q: Find an equation of a plane passing through the points (1, –1, 7), (3, 2, –20) and perpendicular to…
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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…
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Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.
A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…
Q: Find the distance between the point (2, 0, 1) and the plane 2x - 3y + 6z = 6.
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Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…
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Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x + y – 2z…
A: Given:
Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane - 6x + 8y – 10z - 4 = 0 are in…
A: We find out the results by using vectors in 3D
Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…
A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…
Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is
A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.
Q: Find a scalar equation of the plane that contains the linex = 1 + t, y = 2 − t, z = 4 − 3tand is…
A: Given,The plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t.So, we can say that the…
Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…
A: The equation of the plane is 2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…
Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…
A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.
Q: Find the standard equation of the sphere with center (-6, 2, 7) that is tangent to the plane given…
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Q: Find the equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25
A: The equation of the sphere: - The general equation of a sphere is (x – a)2+(y-b)2+(z-c)2=r2 if (a,…
Q: Find the points on the hyperboloid 9x^2 - 45y^2 + 5z^2 = 45 where the tangent plane is parallel to…
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Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…
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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.
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Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.
A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…
Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.
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Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…
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Q: Find the equations of planes that just touch the sphere (x−5)^2+(y−3)^2+(z−1)^2=9 and are parallel…
A: Solution Given (x−5)^2+(y−3)^2+(z−1)^2=9 (a) Parallel to the xy-plane: ( z-1)2= 9 z - 1= | 3…
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: 3. Find the equation of the plane parallel to the plane with equation 18x + 6y – 5z = 0 and passing…
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Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane – 6x + 8y – 10z 4 = 0 are in…
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- What is the equation of a plane where 1 of these spheres would be on one side of the plane and the other sphere would be on the other side of the plane : (x-2)2+(y-1)2+z2=1 and (x-1)2+y2+(z-4)2=0.36If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of x+y+zFind the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0
- Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the line to the hyperbolaConsider the hyperboliode H defined by the equation: x^2+y^2−z^2=1 and the point P0=(1,4,4) in H. Mark the alternative that contains the director vectors v1 and v2 of the two lines that pass through P and are entirely contained in H.Match the description of the conic with its standard equation. Hyperbola with vertical transverse axis (x − h)2 a2 + (y − k)2 b2 = 1 (x − h)2 = 4p(y − k) (y − k)2 a2 − (x − h)2 b2 = 1 (y − k)2 = 4p(x − h) (x − h)2 a2 − (y − k)2 b2 = 1 (x − h)2 b2 + (y − k)2 a2 = 1
- 7. If 1x, y2 are the coordinates of a point P in the xy-plane,then x is called the__________________ of P, and yis the__________________ of P.Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 - 2z^2 = 2.an equation for the plane tangent to the graph of z=9-6x^7+3y^3 at the point where x=1 and y=2 is: