2 ·Prove that at (xp ₁ %) the point of intersection of three confocals 2 ہے and he osculating plane of the curve of Σ Ti + Ti + T: + = 1, = intersection of the first two is given by ==

Q: Find the tangent plane to the equation z = z = 3x² + y² + 4y at the point (1, 0, 3)

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Q: Draw the contour curves for h (x, y) _y²+x² -1+2x and c = 0, 2, 4.

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

A:

Q: Q4\ Graph the curve r=1-cosx in Cartesion xy - plane

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Q: Q3) Determine slope of a curve y = x + 2 at p(1,3) and q(3,11)

A: Slope of a curve : The slope of a curve y=f(x) at a point P is the slope of the tangent at that…

Q: Let C be the upper half of the circle of radius 3 centered at (0, 0). Let f (x, y) be the square of…

A:

Q: What does it mean for two families of curves to be mutually orthogonal?

A: Two families of curve are said to be mutually orthogonal if they intersect at right angles. Angles…

Q: A variable straight line is drawn through the point of intersectio straight lines x / a+y/b = 1 and…

A: Given lines arexa+yb=1               ....(1)and  xb+ya=1               ....(2)Solving (i)and(ii) we…

Q: Show that the parametric curve r(t)= , t [-1,1] is smooth and compute its lengh

A: The given parametric curve is: r(t)=t1+t2, 11+t2 ;          t∈-1, 1

Q: O Differniate the function after a di fferewt form first rewirming the functio^ * Dont use Product…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature…

A: To find where the temperature on the disk is the greatest, we need to find the maximum value of the…

Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: Find the tangent plane to the equation z = 5x² + 3y² − 3y at the point (5, 4, 161) z =

A:

Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

A:

Q: A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1…

A: We use midpoint formula here.

Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

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Q: 5) Find the distance between the pole and the point (r, 0) = (-1, ). %3D

A: A detailed solution is given below.

Q: Find the parametric equation to describe the following curve: b) the part of x = 2y^2 - 1 from…

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