(a) Derive the analogs of Formulas (12) and (13) for surfaces of the form
(b) Let
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- 5. a) Find parametric equations for the tangent line to the curve of intersection between the paraboloid z = x²+y² and the ellipsoid 4x² +y²+z² = 9 at the point (-1,1,2). Also, find a vector function that represents the curve of intersection. b) Find parametric equations for the line tangent to the curve of intersection between S₁: x² + y² = 4 and S₂ : x² + y² - z = 0 at the point (√2, √2,4). Find a vector function for the curve of intersection.arrow_forwardAssume that the second partial derivatives of the surface X = x(0, 4) are given by Xo4 = 0, X4 - e, + 2pes X00 = 0e, – 2pe,, And has the unit normal vector N = sin0e, + cos o ez. Then the second fundamental form coefficients L, M, and N of the surface are given by L-O sin -2o cos . M-0,N- sin ở + 20 cos o L = 0 sin 0, M = 0, N = sin 0 The above answer The above a nswer L= 0 sin 0, M = 0, N - 20 cos o I. - O sin 0. M- 0. N- sin 0 + 20 cos o The a bove ans wer The above a ns werarrow_forward4. Consider the vector function r(z, y) (r, y, r2 +2y"). (a) Re-write this vector function as surface function in the form f(1,y). (b) Describe and draw the shape of the surface function using contour lines and algebraic analysis as needed. Explain the contour shapes in all three orthogonal directions and explain and label all intercepts as needed. (c) Consider the contour of the surface function on the plane z= for this contour in vector form. 0. Write the general equationarrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage