Consider the ellipsoid 4x2 + 2y2 + z² = 27. Find all the points where the tangent plane to is parallel to the plane 2y - 8x - 3z = 0.

Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

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Q: Q2/ Find the Parametric aned standand equatior of the line Hhat passer through Points (-2,1,0)…

A: The equation of line passing through given two points is given as follows:

Q: Find the equation of the plane passing through the point P(2, -1, 3) and perpendicular to the line…

A: We have to find the equation of the plane passing through the point  and perpendicular to the line…

Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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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: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

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Q: Suppose C is the line y = 5-2x in the xy-plane. Determine parametric and Cartesian equations of the…

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

Q: Find the distance between the skew lines with parametric equations x=3+t, y=2+6t, z = 2t, and…

A: Given :x=3+ty=2+6tz=2tx=2+2sy=4+14sz=-2+5s

Q: nd the point (a, p) on the ellipse 4x adrant, so that the area enclosed by the

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Q: Find the distance from the point (1,1,1) to the plane 2x+2y+z=0

A: Solution :-

Q: Find the parametric equations of the line tangent to the curve of intersection of the surfaces x² +…

A: The tangent to the intersection of the curves: f(x, y, z)=0, g(x, y, z)=0 is parallel to the vector:…