please do part a and c only. The part c is the priority
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please do part a and c only. The part c is the priority. Thank you.
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- Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?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 = 36Given the surface 9x^2 − 4z^2 = 9y. Find its traces on each coordinate plane and on the planes y=4, y=-4. Give the vertices and sample points of the parabolas and hyperbolas formed.
- Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of one sheet, a hyperboloid of two sheets, a cone, a circular cylinder, an elliptical cylinder, or a parabolic cylinder, and identify the axis of symmetry as the x-axis, the y-axis, or the z-axis. 7y^2+7z^2=1 −9x^2+3y^2−z^2=0 4x^2+8y^2−z=0−7x^2−4y^2+z^2=1 3y^2−4x^2−7z^2+1=0Given 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.Use traces to sketch and identify the following surface 25x2+4y2+z2=100
- For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola. (a) x = 0 (b) y = 0 (c) z = 1Determine the points on the surface y2+z2−x=8 that are closer to the origin.Determine the points of the surface M: x²+y²+z²-4x-4y+6=0 for which the distance from the axis Z has an extreme value.
- Show the complete solution for the following problems.Let S be the surface with equation given by 4x2- 9y2 = 9(z2 + 4).I. Find an equation of the trace of S on each of the coordinate planes and on the planes x = ±3√ 2. Determine if each trace is empty, a point, a (pair of) line(s), a parabola, an ellipse, or a hyperbola.II. What type of quadric surface is S?III. Using the traces obtained in I, provide a hand-drawn sketch of S. Label all important points (e.g. vertices) found on each trace.IV. View S as a surface of revolution. Find an equation of a generating curve on the xy-plane which, if revolved about the x-axis, will result to S.Classify each of the following quadric surfaces as either an ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets, elliptic cone, elliptic paraboloid, or hyperbolic paraboloid. Record the values of a, b, and c for each quadric surface. a) 2z - x^2-4y^2=0 b) 6x^2+3y^2+4z^2=12 c) 4x^2+y^2-4z^2=-4 d) y^2-x^2-z=0 e) 9x^2+y^2-9z^2=9 f) 12z^2-3x^2=4y^2Given 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.