5. Let C be the curve of intersection of the hyperbolic paraboloid z=x² - y² and the cylinder x² + y² =1. (1) Find the curvature of C at the point P(1,0,1). (2) Find the osculating plane at the point P(1,0,1).

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A:

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A: 1 )Equation of a Parabola:The standard equation of a parabola in the xy-plane is given by  where a…

Q: 4. Consider the curve in the plane defined by r3+y3 = 6xy. %3D (a) Find for any point (r, y) on the…

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Q: 10. The point (1, 2, 5) is on the quadric surface z = x² + y². Is this point closer to the line with…

A: Given   1. Point on the quadric surface z=x2+y2 is 1,2,5 2. Parametric equation of the line is…

Q: TRUE OR FALSE. A plane curve C defined by the parametric equations x = f(t) and y = g(t), where t is…

A: check the given statement is true or not.

Q: Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2).…

A: Solving

Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

A:

Q: Find the curvature of the curve r (t) = (- 5+ 4t, 1+ 3t, 5t) at the point t - 7.

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Q: Solve the following Differential Equation

A: Given the differential equation              (3x+4y-7)dx+(9x+12y+1)dy=0.

Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

A:

Q: 1. Find the Curvature at the Point (0,3) above the ellipse x = 4(ost, y = 3 sint

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Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

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Q: 4. Consider the parametric curve x = cost, y = sin cost, te [-T, π]. (a) Show that (0,0) is a point…

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A:

Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?…

A: The solution is given as follows