paraboloid z= 1 - (2x^2) -y^2 and plane z + x + y =4 find the shortest distance between them

Q: AP is perpendicular to PB, where A is the vertex of the parabola y^2 = 4x and P is on the parabola.…

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Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: Find the distance between two planes if they are parallel x+2y+3z=6 and 2x+4y+6z=5

A: Solution:GIvenx+2y+3z=6  and 2x+4y+6z=5To find the distanceFormula:If θ=0°  then the planes are…

Q: The hill has the shape of a cone, which in the XYZ system has the equation z = 4 - sqrt(x^2+y^2) A…

A: Given that hill has the shape of the cone given by z=4-x2+y2 and the tourist moves uphill whose path…

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: Given the parabola x^2=4y, a line passes through point A (4,4) and the focus of the parabola. Find…

A: Topic:- Parabola

Q: Let there be two parabolas y^2 = 4ax and y^2 = -4bx (where a not equal to  b and a, b > 0). Then…

A: Let us consider that the line parallel to the common axis be y=h.then the co ordinates of A and B…

Q: ind point P and Q on the parabola y=(-x^2)+1 so that the triangle ABC formed by the x-axis and the…

A: Given that the curve is                         To find point P and Q on the given parabola, so that…

Q: The following line intersect with the xz-plane. What is the point? x = -2; y = 4+2λ; z = −3+2

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Q: AP is perpendicular to PB, where A is the vertex of the parabola y^2 = 4x and P is on the parabola.…

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Q: The figure shows two lines: One line is the secant line between the origin and a point P on the…

A: Given the figure:

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x - 6y + 2z = 5

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Q: The shortest the the poin X+2y+2z=13

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.