Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to two

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

A: Note that here we have to extremize x2+y2+z2 , whch is eqivalently ,to extrimize x2+y2+z2.

Q: Consider the paraboloid given by the equation z = x^2 + y^2. Find the coordinates of the vertex and…

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center. The given…

Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: Find the perimeter of the ellipse x2/a2 +y2/b2 = 1, where a > b > 0.

A: The perimeter of Ellipse with Radii a and b is given by: In our question the radii is a and b Hence…

Q: The cylinder x² + y² = 25 intersects the plane x + z = 5 in an ellipse. Find the point on such an…

A: Given:The cylinder is: .The plane is .The cylinder intersects the plane in an ellipse.

Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: Write the quadratic surface x2-y2+4z2+2x+4y+1=0 in standard form.

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Q: Find the points on the ellipse  (x2/9) + y2 = 1 closest to the point (2, 0).

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

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Q: What is the center of x² + y² – 6x = -4y + 68?

A: given equation of circle  x2 +y2-6x=-4y+68  x2+y2-6x+4y-68=0 Now compare with x2+y2+2gx+2fy+c=0…

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

A: