A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O 24x+21y=504, Os xs 21 O x²+y²=504, OS xS 504 O 21x2+24y2=1, 0s xs 24 O 21x+24y=1, Os xS 24 O 21x+24y=504, Os xs 24

Q: List all of the points (x, y) on the parametric curve t° + 4t, y = 6t? where the tangent line is…

A: Given that, Parametric equation of the curve are following, x = t3 + 4t,      y = 6t2 and the…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

Q: Find the equation of the line tangent to the parametric curve (pictured below) defined by I=, y=t+t…

A:

Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: x = 2t2 – C : 3t + 1 y = et²-1

A:

Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x - 5 between…

A: formula:

Q: 2) Graph the x, y-curve described by the parametric equation by eliminating t from the equation. x =…

A:

Q: 15. Find the radius of curvature at 0 = -n of the parametric equations x = 3(0 + cos 0), y = 3(1 –…

A: For the parametric curve x=x(θ), y=y(θ)Curvature K=|x'y''-y'x''|[(x')2+(y')2]32Radius of…

Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –…

A:

Q: 27. Show that the curve with parametric equations x = t cos t, y =t sin t, z = t lies on the cone z²…

A: To Show: i. Show that the curve with the parametric equationx=tcost, y=tsint, z=t  lies on the…

Q: Which of the following are parametric equations for the ellipse given by + y? 9 1? Choose all that…

A: Idea: By using parametric equation of ellipse we can solve this question .

Q: Suppose parametric equations for the line segment between (1, - 5) and (2, – 6) have the form: Sz(t)…

A: Given xt=a+btyt=c+dt if curve starts at (1 , -5) when t=0 and ends at (2 , -6) at t = 1 then we have…

Q: A curve is defined as the parametric equations: 1 x = acose, y=-asin 0, 0<0< 2n dy where a is a…

A: on solving this we get

Q: 16. Sketch the parametric curve x = Vt, y= sin t, 0<t< 2n. (b) (a) 1.0 (c) 101 1.0 0.5 0.5 0.5 05 10…

A: The graph of the parametric curve x=√t, y=sint , 0≤t≤2π is given as below,

Q: z = In(x²y*) + / x² + y²

A:

Q: Find the length of arc of the curve given by the parametric equations x = t°, y=t² from the point…

A: Arc length is given byL=∫abdxdt2+dydt2dt

Q: A curve is defined by the parametric equations (t) = 8 cos(6t) and %3D y(t) 4 sin(-4t). Find . %3D

A: We have to find derivative

Q: Determine the area under the parametric curve defined by the equations x-t2-4 and y=t on the…

A: To find: The area under the parametric curve x=t2-4 and y=t on the interval 0,3. Formula used: The…

Q: Consider the parametric curve defned by r=3+5t and y=1+ Over which values of y does t curve has a…

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: Graph the curve with parametric equations x = sin(t), y = 3 sin(2t), z = sin(3t). H0.0 y -0.5 0.5…

A: The graph will look like this:

Q: Chapter 13, Section 13.7, Question 031 Find parametric equations for the tangent line to the curve…

A:

Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

A:

Q: Find the exact value of x²y³z ds, where C is the curve with parametric equations x = e-t cos(5t), y…

A:

Q: ) (i) Find the parametric equations for a smooth curve, C: x= 4z, y = -3z that joins two points,…

A:

Q: a) Compute the enclosed area and length (from 0 to 2pi) of the parametric curve given by 3, 3, x = A…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Let C be the parametric curve given by 1²+2t +8, C: y= cost +1, An integral for the area of the…

A: Given parametric curve is,

Q: 9. Find the exact length of the parametric curve for the given interval. x = 4t 2 - 3, y = 3t, 0 St5…

A:

Q: A parametric curve is defined by : I) x = 5sin(t ) – 2; y = 1– 3 cos(t ) ; 0sisa

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

Q: Which of the following is Parametric equations for the line passing through the origin and A(1, 0,…

A:

Q: Find an equation of the line through (0,0,0) that is parallel to the e parametric equations x(t) = 2…

A: To find out equation of any line we need one point on the line and a vector which is parallel to the…

Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

A:

Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: Find the arc length of the curve on the given interval. Parametric Equations x = 5t + 5, y = 7- 2t…

A: The parametric equations of the given curves are   x=5t+5,  y=7-2t and the given interval is -1≤t≤3…

Q: Find the length of the curve having a parametric equation of x= 2cos³0 and y=2sin²0 from 0-0 to…

A:

Q: a) Find the are length of the parametric curve x = B(t. sint), y = B(1+ cost), in the range 0 sts,…

A:

Q: Which of the following are parametric equations for the ellilpse glven by 9. + y? = 1? Choose all…

A:

Q: Find a rectangular equation for the plane curve defined by the parametric equations. x = 6 sin t, y…

A:

Q: Find the length of the parametric curve C {(x(t), y(t)) : t E 1} x(t) 4cos(t), y(t) = 4sin(t), with…

A:

Q: Eliminate the parameter in x = -t +2t and y =t-4 and then identify the parametric curve and sketch…

A:

Q: A curve is defined by the parametric equations z (t) = at and y (t) = bt, where a and b are…

A: Given,  We have  xt = at   and yt = bt  ;  where a and b are constants.  We have to find the length…

Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x – 5 between…

A:

Q: Consider the curve. (금) 2 = 1 19 + Identify all possible parametric equations for the given curve. O…

A: In this question, we can check one by one parametric equation in the given curve.

Q: 9.) a. Find the parametric equations for the tangent line to the Curve at' the Specific point. X =t°…

A:

Q: Find the length of the parametric curve defined by x=r°, y=t- for 0st<1 7.

A:

Q: a) A curve is given by the parametric equations 1 where 1 <t<3. t' I = 2 lnt and y = - i. If L is…

A: We need to find length of curve.

Q: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

A:

Q: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

A: