Find orthogonal trajectory to the curve given by r = a(1 + cos θ)

Q: 5) Find the orthogonal trajectory of the family of curve given by y = In(r+b) %3D

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Q: Find parametric equations for the tangent line of the curve r(t) = (3+ 3/7, to – 5t2 + 4, 3t³ + 2t²…

A: Find the parametric equations fot the tangent line

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find the slope of the tangent line to the parametric curve [x = 4 cos(t) y = 3 sin(t) at the point

A: A detailed solution is given below.

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: The equation of the tangent line to the parametric equations, x =t +sint, y 4t-cost att 0 is y = -1…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: Find an equation for the tangent line to the curve given parametrically by x(t) 2t, y(t) 4t2 +t+ 3 =…

A: we want to find the tangent lines to theparametric equations given byx=f(t)  y=g(t)The equation of…

Q: Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+2 sin 6 at…

A: Given that: x=2-3cosθ and y=3+2sinθ

Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Find the derivative dydx of the polar function r=3+2cosθ at θ=π6.

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Q: Find parametric equations for the tangent line at the point (cos(−4π/6),sin(−4π/6),−4π/6) on the…

A: Given parametric equation of given curve is x=cos(t), t=sin(t), z=t Differentiate with respect to t.…

Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

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Q: Find the equation of the tangent line to the parametric curve at (1,3). 2=1+ Int y =t² +2

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Q: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (-1/2,-V3).

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Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: The parametric equations of a curve are given by = In (Vi +1) and y = cosh" (21). dy Find the…

A: The derivative of the function u=f(v) is the measure of how fast the function f is changing with…

Q: Find the exact slope of the tangent line to the parametric curve at the point where y = 2 sin(t) t =…

A: x=8 cos (t) y=2 sin (t)

Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 – 4t +…

A: We find out dy/dx .then we find out value of t at given points and then find slope of tangent line…

Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…

A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

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Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

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Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: find the orthogonal trajectory of the family of curves r^n = a sin n theta

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Q: Find the slope of the tangent line to polar curve r=5sinθ at the point (5/2,π/6).

A: This question is related to Straight line, we will solve it using given information.

Q: Find an equation of the tangent(s) to the curve with parametric equations x = t cost, y = tsin t…

A: Given- x=tcost , y=tsint To find - To find the equation of tangent to the curve with given…

Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

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Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the…

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Q: Find the slope of then tangent line to the parametric curve t t2 + 25, y 6. at t = -1 and t = 1…

A: Shown below

Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1 + √t, y = e^(t^2)…

A: Given parametric equation of curve x=1+t   y=et2we want to find equation of tangent at  ( 2, e)

Q: x = 1+ vt, y = et X =1+1 Y. %3D

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Q: The parametric equations of a curve are given by 1 = In (Vi +1) and y= cosh(2t). dy when t = 1. dr…

A: According  to question given thatx=ln(t+1)y=cosh-1(2t)

Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: Sketch the cardioid curve r = 1 + cos θ.

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Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: ) Find the equation of the tangent line (in terms of x and y) to the parametric curve at the given…

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Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

Q: Find the derivative dydx of the polar function r=sec(2θ) at θ=π4

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Q: Consider the parametric curve C defined by x = x (t) and %3D y = y (t). (a) How do you find the…

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Q: Find the orthogonal trajectory of y=c cos x.

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