The figure shows a fixed circle C, with equation (x – 1)? + y? = 1 and a shrinking circle C, with radius r and center the origin. P is the point (0, r), Q is the upper point of intersection of the two circles, and R is the point of intersection of the line PQ and the x-axis. What happens to R as C, shrinks, that is, as r→ 0+? y. R

Q: Let the curve C be the mirror image of the parabola y" the line x+y + 4 = 0 If A and B are the…

A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: The tangent to the circle x? + y? +3 x+ 3 y = 38 at the point (2,4) is Select one: O 11 y + 7x = 18…

A: According to the equation, we need to calculate the equation of tangent to the circle at point…

Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

Q: Solve the problem in an unknown interval z E [0, a] using transversality condition J = min y(1),a.…

A: Solution:-

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: 6. Determine the equation of the circle whose center is at (4, 5) and tangent to the circle whose…

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

Q: 1) Evaluate F dr where F(r,y) = ri and C is the half of the circle %3D ²+y 3 16 lying below the…

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Q: 35. In the xy-plane, the circles with equations (x-3)² +y² = 11. and (x+2)² + y² = r² |3D %3D 2re…

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Q: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: Find points P and Q on the parabola y = 1 – x² so that the triangle ABC formed by the x- axis and…

A: We have △ABC is an isosceles right angle triangle. So the interior angle at B and C must be 45° The…

Q: Find an equation of the line which is tangent to the circle z + y - 4x + 6y – 12 = 0 at the point…

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Q: Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate…

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Q: Use Green's Theorem to find (8y + x) dx + (y + 2x) dy, where C: The circle (x - 4)2 + (y-3)2 9 541…

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Q: Evaluate x ds, where Cis с a. the straight line segment x = t, y = = 737₁1 3' b. the parabolic curve…

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Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

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: The tangent to the circle x? + y? +3x+3 y = 38 at the point (2 ,4) is Select one: O11 y- 7x = 58 011…

A: Equation of the circle is : x2 + y2 + 3x + 3y = 38 at point (2,4)

Q: a. Find the length of the arc of the semicubical parabola ay=x' , from x= to x= 5a.

A: Arc length of the curve

Q: Given that the line y =r- b is an asymptote to the ar curve y a,b €R,r = 1, then b = I-1 -1-a B 1-a…

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Q: Verify Green's theorem for $[xy² dx + x²y dy], where y is the circle x? + y² = 4.

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Q: 6. Show that the line with equation y = 3x – 5 is a tangent to the circle with equation x² +y? + 2x…

A: Equation of line : y=3x-5 Equation of circle : x2 + y2 +2x -4y -5=0 We have to prove that the line…

Q: The Cartesian equation for the curve z = sect, y= tant, -<t< is Select one: O y=z. O none of these…

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Q: (y - eCos(e25! dx + (x2 + y+1) dy, where C is the circle r = 2.

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Q: The cartesian equation of the curve x= vt ,y 1-t is: (a)y = 1– x2, x2 0 (b)y = 1-x,x N0 %3D (c) x =…

A: Eliminate t then solve

Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

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Q: Find the center and radius of circle x“ + y° - 2x-4y+1=0. Prove thot (0

A: I am solving question 1. if you want other question to be solved then repost.

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

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Q: Let P be a point at a distance d from the center of a circle of radius r. The curve traced out by P…

A: Given:

Q: Evaluate f. y3 dx - x3 dy where c is the circle x2 + y2 = 4

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Q: 29.Consider the circle (x + 1)² + (y – 3)² = 116. Find an equation for the tangent line drawn to the…

A: Since you have asked multiple unrelated questions in a single request we would be answering only the…

Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: The siope of a line tangere to the curve y=fx)at(3 4) 0f iz cists) equais

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Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

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Q: The equation of a circle in the zy-plane is 2 + 4x + y? – 10y = 20. If the line z= k intersects the…

A: Consider the equation of circle in xy-plane given by x2+4x+y2-10y=20 If the line x=k intersect the…

Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: (i) On the same diagram, sketch the eurves y? =-* and y x (ii) Find the exact r-coordinate of the…

A: The solution is given below in the next step:

Q: What is the equation of the circle concentric with circle(x-2)2 + (y+1)2 = 5 that is tangent to the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

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Q: 3. Find an equation of the circle with center at (5, –6) that is tangent to the y – axis in the form…

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Q: Consider the intersection curve C in the first octant, between the surfaces s1: 2 = 1- r? S2 : 2 +…

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Q: If C1 is the segment connecting (x1, Y1) to (x2, Y2), find | x dy – y dx in terms of the four…

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Q: Evaluate S,lz| dz for the curves C1 and C2, both of which begin at a = 1 and end at b = -1. The…

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Q: Find the maximum and minimum values f(1, y) = zy takes on the circle %3D r + y² = 12.

A: Lagrange multipliers method: First solve the following systems of equations: ∇fx,y=λ∇gx,y. The…

Q: The tangent line to the graph of y = In(x² – 1) is perpendicular to the line z + y = -1lat the point…

A: Given: y=lnx2-1 and x+y=-1 Concept Used: Slope of perpendicular lines are negative reciprocal to…

Q: ² fx ds, where C is с t a. the straight line segment x = t. y = from (0,0) to (16,4) b. the…

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