Sketch the 3D graph of the following functions: Surface z= (x-1)² + (y+ 2)² + 3 Surface 4x?+4y²+z²+8y-4z=–4 (i) (ii)

Q: The curve y + 22 = 25 is translated to a new position in the plane and the equation of the new curve…

A: Suppose y+x2=k is any function, where k is constant. Then, in the new translated function…

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: y -0.5 -0.75 1.5 0.5 0.25 -15 |(1) (2) (3) |-1.75 1.5 -0.5 0.5 0.25 -0.5 y y -0.5- 0.5 -이125- 0.5 -1…

A: Matched surfaces and contour diagrams:   Surface              Contour diagram (a)…

Q: 9. Find the vertex and focus of the parabola whose equation is 24x = -(y – 6)² + 192 O V(-8, –6),…

A:

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

A:

Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

A:

Q: a(t) Write the Cartesian equation of the line given by the parametric equations < y(t) 1- 9t -1+t.…

A:

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: The paraboloid z = 8-x-x²-3y2 intersects the plane x = 2 in a parabola. Find parametric equations in…

A: The equation of the paraboloid is given as z=8-x-x2-3y2. The paraboloid intersects the plane x=2 in…

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it. (a) z23x²+4y²…

A: We have to reduce the equation in standard form, classify the surface and sketch the surface.Note:…