If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = C, where f(x) ≤ c, then one can prove that a formula for the area of the resulting surface is S b = [ 2π[c − f(x)] √/1 + [ƒ′ (x)]² dx. Find the area of the surface generated by rotating the circle x² + y² = µ² about the line y = = r.

Q: 2. Find the equations of tangents that can be drawn from the origin to the circle x² +y-2x+8y+2=0.

A: Given below the detailed solution

Q: b) The curve y = }(r² – 2 In r), 1<r< 4, is rotated about the y-axis. Find the area of the resulting…

A:

Q: The arc of the parabola y =  x sq.  from ( 1,1, )  to ( 2, 4 )  is rotated aboutthe  y -axis. Find…

A: Given:The arc of the parabola y=x2 is rotated about the y-axis from 1,1 to 2,4. We have to find the…

Q: (b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the…

A: Consider the equation of the circle The graph can be plotted for the circle as

Q: B- Find the area of the surface generated by revolving the curve y = √2-x² about x-axis

A:

Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: Find the area of the surface generated when the given curve is revolved about the y- axis. y =, for…

A: Answer is optional B

Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

A:

Q: 6. Show that the area of the triangle intercepted from the co ordinate axes by the tangent to the…

A: We have to show that the area of the triangle intercepted from the coordinate axes by the tangent to…

Q: Two circles have equations of x2 + y2 – 4x – 4y + 4 = 0 and x2 + y2 – 4x + 8y + 4 = 0. Compute the…

A: