Given z39-24x is a curve in the xz-plane. If the equation of the surface generated by revolving the curve about the z-axis is ax+ay2+ayaatasr+z+g=0, then (Notice that you have to write the surface equation where the coefficient of z is one.)
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- Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a surface of revolution) on the yz-plane.Find the points on the surface z2 = xy + 4 closest to the origin.Consider the following surface: z = x2 - (y2 / 4). By hand, without any graphical utilities, find an equation for the intersection of the surface and a plane containing the points (1, 0, 0), (2, 4, 0), and (-1, -1, -1).
- Given the expression x⁴-3x+7=y³ on the interval [3,5], determine the surface of revolution if it is revolved about x=-3.Given 3x^2 +6y^2-z^2 = 36. Find and sketch each of the traces. what is the quadric surface is represented by 3x^2 +6y^2-z^2 = 36The given curve is rotated about the y-axis. Find thearea of the resulting surface. y = 1 -x2 0≤ x ≤1
- Given the surface 9x^2 − 4z^2 = 9y. 1. Find its traces on each coordinate plane and on the planes y=4, y=-4. 2. Give the vertices and co-vertices of the hyperbolas formed. 3. Give vertices and sample points of the parabolas formed.Which graph shows the intersection curve, in the first octant, between a cylinder of equation: (x − 3)2/a2 + (z − 2)2/b2 =1, where a > b > 0, with the equation plane z = 4 − ysketch the given surface. x2 − 4y2 = z
- At what points does the curve r(t) = ti + (5t − t2)k intersect the paraboloid z = x2 + y2The exact solution of the 2q(z - px - qy) = 1 + q^2 equation and by using this solution,Find the integral surface through the curve y: 2x = y^2 + z^2, y + 1 = 0At what points does the curve r(t)=(t,t,14t) intersect the surface z=x2+3y2?