13. r= 2 cos 0 14. r= 3 sen 0

Q: Consider the following set of parametric equations. Use our ‘Analysis of Intervals’ technique to…

A: Solve the following problem

Q: Write Parametric Equations to Represent a Curve for the given curve for the given definitio:

A: In question number 32, we are asked to form only parametric equations, that means equation of x and…

Q: What is the eccentricity of the curve x = sint and y = cos2t?

A: x=sint⇒x2=sin2t         1 y=cos2t             2 Adding booth equations- x2+y=sin2t+cos2t⇒x2+y=1

Q: hinormal of the curve traced by Q makes an angle tan- (cp/o V(c2 + o?)} with PQ.

A:

Q: Convert the equation r = 14 cos 0 to Cartesian coordinates. Describe the resulting curve.

A:

Q: In the given equation as follows , use a graphing utility to graph thecurve represented by the…

A: Given parametric equations

Q: Plot the curve r = 1+sin 8. Then find the length of the curve.

A:

Q: ind the Cartesian equation of the curve C traced out by a point whose coordinates, in terms of a…

A: given curve c is traced by point   a cosθ  , b sinθ now Consider     x= a cosθ     ,    y = bsinθ⇒…

Q: The curves (t) = and i,(s) = intersects at the origin. Their angle of intersection is 0 = %3D

A:

Q: Find the circumference of a circle described by the parametric equations = 7 cos 0 and y = 7sin 0…

A: The formula L=∫dxdθ2+dydθ2dθ is formula for length of arc in polar coordinates. As we go along the…

Q: a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and…

A:

Q: a) Eliminate the parameter to find a Cartesian equation of the curve. b) Sketch the curve and…

A: From x=12cosθ we get  cosθ=2xFrom y=2sinθ we get sinθ=y2Using the Pythagorean identity we…

Q: Compare the equation r=2 with its equation in rectangler coordinates. In which coordinate system is…

A: The given equation is r=2.   Square both sides of the equation. r2=22=4   Substitute 4 for r2 in the…

Q: x = 2 cos(?),    y = 3 sin(?),    −pi/2 ≤ ? ≤ pi/2 Eliminate the parameter to find a Cartesian…

A: Given that x=2 cost and y=3 sin t where -π2≤t≤π2. To eliminate the parameter ,divide first…

Q: Find the lengths of the curves given by the polar coordinate equations r = 8 sin3 (θ/3), 0≤ θ ≤ π/4

A: Given data: The polar coordinate equation is r=8 sin3(θ/3). *The limit of the function is 0≤ θ ≤…

Q: Find a Cartesian equation for the curve and identify it. r = 9 cos(8) circle O parabola O limaçon O…

A: here we have,  the polar equation of the curve is ,  r=9cos(θ) ................(1)

Q: Sketch the curve represented by the parametric equations x = 8 cos θ,            y = 8 sin θ…

A: given: the parametric equations of the curve are: x=8cosθy=8sinθ

Q: Graph the parametric equations (x(t) = cott ly(t) = sin² t

A:

Q: Consider thne par. x = 2 - 1, y = t + 2, -3 sts3 (a) Sketch the curve by using the parametric…

A: b) Given parametric equations x=t2-1, y=t+2, -3≤t≤3. Solving x=t2 -1 for t we get,t=±x+1 for…

Q: a) Eliminate the parameter to find a (simplified) Cartesian equation for this curve. (b) Sketch the…

A: We have to find a Cartesian equation for this curve and sketch the parametric curve.

Q: Find a Cartesian equation for the curve and identify it. 12 cos(20) = 1 o ellipse o limaçon circle o…

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate…

A:

Q: Idatify the sy mnctries of the curves and sketehit after. V=I+ Cose Y=+Sin9 バ= HZ Sm 9 ノ

A:

Q: x = 1 – t², y = t – 2, –2 <t< 2

A:

Q: 8- For the curve whose Cartesian equation is: (x2 + y?)3/2 = 2x? a. Find and simplify the equation…

A: The given equation is x2+y232=2x2

Q: Sketch the line and find Cartesian equations for it. r cos(u + pi/3) = 2

A: Given equation: r cosu + π3 = 2

Q: Find a Cartesian equation for the curve. r = 8 sin(0) + 8 cos(0) Identify the curve. o ellipse…

A:

Q: Find points P and Q on the parabola y = 1−x^2 so that △ABC formed by the x−axis and the tangent…

A: Given, curve

Q: Name the type of basic curve that the following pair of equations represents: x = 2 cos(3t), y =…

A:

Q: Find a Cartesian equation for the curve and identify it. 2 cos(20) = 1 O limaçon O circle O parabola…

A: Given curve  r²cos(2theta) = 1

Q: The planet XYZ travels about the star ABC in an orbit that is almost circular. Assume that the orbit…

A: Given, Radius(r)= 77000000 mi We know that, Circumference of the orbit= 2pi(r)= 2pi(77000000)…

Q: Sketch the curve represented by the parametric equations x = 2 + 3 cos θ andy = 2 sin θ. Eliminate…

A: The curve represented by the parametric equations x=2+3cosθ and y=2sinθ is shown below,

Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. rsin 0 =7 The…

A:

Q: . Consider the curve given by the equation 2(x+y)=5siny. b)Determine the concavity of the curve for…

A: Apply second Derivative test

Q: Consider the following. x = tan2(0), y = sec(0), - T/2 < 0 < T/2 (a) Eliminate the parameter to find…

A: Explained below

Q: The curves with equations x  =a sin nt , y = b cos t are called Lissajous figures. Investigate how…

A: Given, Lissajous figures x = a sin(nt) and y = b cos(t) We have to investigate how the curve varies…

Q: 3. The two curves r,-1-cose and razcose are intersecting at angles: A. (-5. B. (. c.).

A: Explanation of the answer is as follows

Q: Consider the following. x = et - 6, y = e2t (a) Eliminate the parameter to find a Cartesian equation…

A:

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = cot(t) y =…

A:

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for involving…

A:

Q: For the following plane curve, find a rectangular equation. x-t", y 4 In t for t in (0,00) What is…

A: given,       x=t4y=4logt

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = sect, y =…

A: We have to find a rectangular coordinate equation for the given curve.

Q: Find parametric equations that define the curve starting at (6.0) and ending at (7.9) as shown. Let…

A:

Q: Given x= sin 0, y = cos 0, n <o< 2n a) eliminate the parameter to find the rectangular equation of…

A:

Q: Question: Find the points of intersection of the given pairs of curves. ?=−2sin?,?=2(1+sin?)

A: Consider the given curves, y=-2sinx and y=21+sinx at the point of intersection, both the curves pass…

Q: 9. The Cartesian equation of the curve r=- is 1-cos(0) (Write your answer in the following form y?=…

A: For polar form,  Substitute  r=x2+y2;cosθ=xrsinθ=yr

Q: Given the parametric equation: x=2sint-3, y=2cost+5, 0 less than or equal to t less than or equal to…

A: Given x=2sint-3, y=2cost+5   , 0≤t≤2π

Q: Find a Cartesian equation for the curve. r = 7 sec(?)

A: Given query is to find the Cartesian equation if the curve.