4. Express the given equations in polar coordinates (a) x=3 (b) x² + y² = 7 (c) x² + y² +6y=0 (d) 9xy=4

Q: 2. For the equation 2x² + 2xy + 2y²-2x-10y+11= 0, eliminate the xy term by rotating the coordinate…

A: Given: The given equation of the conic is 2x2+2xy+2y2-2x-10y+11=0.                      ...........1…

Q: 4. (a) Plot the following points in the same polar coordinates system (b) Convert into rectangular…

A: To convert the polar coordinates r,θ to rectangular coordinates x,y then x=rcosθ and y=rsinθ

Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

A:

Q: Convert to polar form. Then isolate r. (a) x² +y² -9= 0 (b) x² +y = 4x %3D

A: x2+y2-9=0 On simplification, we get ⇒x2+y2=9⇒r2=9         ∵r=x2+y2⇒r2=x2+y2⇒r=3

Q: Replace the polar equation with an equivalent Cartesian equation. r² = 44r cos 0 (x-22)² + y²-0…

A:

Q: Write the given polar equation in cartesian form (in terms of x r – 1= cos 0 = Cos 2- y? – 1 = x²…

A:

Q: 5. Convert the polar equation to rectangular equation of the form y = mx + b. Simplify your answer…

A:

Q: Which of the following represents the rectangular equation x² + y²-5y-0 in a polar equation?

A:

Q: Write the parametric equations as a function of x in Cartesian form. = x = 2t - 1, y = 6 - 3t

A: Given equation are x=2t-1 and y=6-3t

Q: The parametric equations that correspond to T= (2t 1) i- 3vtj+ sin 3t k is %3D

A:

Q: 2. Evaluate the quantity e™ for each of the given values of 0. Give your answer in rectangular form…

A: As per bartleby guidelines we only give first three questions answers.

Q: 3. Find the polar form of the Cartesian equation: x² + y² = (3 + 2x)² %3D

A: Solution-

Q: 2 - y = 2 #8) A) Change equation x 4 to polar coordinates.

A:

Q: Convert the following rectangular equations into polar equations. (a) x² + y² = 2x r = a cos(0); a=…

A: a) x2+y2=2x To convert rectangular equation to polar, substitute x=rcos(θ) and y=rsin(θ) So, the…

Q: 4. Sketch the parametric equations by eliminating the parameter. Be sure to include arrows to…

A: From given equations, we find sin theta and cos theta Then we plug them in the Pythagorean identity…

Q: 1) (a) Convert BOTH of the below equations from either polar to rectangular or rectangular to polar.…

A:

Q: x+4 5 y-2 -5 2+1 1

A: Given the equation is x+45=y-2-5=z+11

Q: 1z2 in polar form. z1 = 5(cos(170)+i sin(170)) : z2 = (1/2) (cos(10)+i sin(10)

A:

Q: Convert the Cartesian equation to a Polar equation. Express your answer as r = 2y –x² = 2y– 3x

A: The objective is to convert cartesian equation to polar equation.

Q: - Change LAxy dydx to polar form.

A: Consider a cartesian coordinate and polar coordinate . Then the relation between these two…

Q: Find a Cartesian equation for the curve given by the polar equation T = 4 sin 0. 73°F 1. (x - 2)² +…

A: We have to find out

Q: 1) (a) Circle ONE of the below equations and convert it from either polar to rectangular or…

A: