Write the equation 23x2 + 26√3xy - 3y2 - 144 = 0; θ = 45° in terms of a rotated x′y′-system using θ, the angle of rotation. Write the equation involving x′ and y′ in standard form.

Q: Convert (2,-pi/6) into its rectangular coordinates

A: We can solve this as follows:

Q: Write the equation x2 - 4xy + y2 - 3 = 0; θ = 45°in terms of a rotated x′y′-system using θ, the…

A: Given: x2 - 4xy + y2 - 3 = 0; θ = 45°

Q: Write the equation in terms of a rotated x'y'-system using θ, the angle of rotation. Write the…

A: Given equation is We know that relation between coordinates (x,y) and (x',y') is Now,

Q: Identify the equation 10x2 + 24xy + 17y2 - 9 = 0 without applying a rotation of axes.

A: We have to identify the equation  10x2 + 24xy + 17y2 - 9 = 0 without applying a rotation of axes.…

Q: 1. Put the following equations in standard form and find the center point and the radius: a) x-2x+y…

A: Given that

Q: b) Find the counter-clockwise angle of rotation of axes to remove the xy term in the equation 12x² +…

A:

Q: form the cartesian parenmetnc equations. x- 3 tom g equation fon. there .2fec o

A: given parametric equations x=3tanθ, y=2secθ⇒tanθ=x3, secθ=y2

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.

A:

Q: Convert the equation 16x2 + 25y? = 400 from cartesian to polar

A: See attached file for a step by step explanation.

Q: When the axes are rotated through an angle 4 π , find the transformed equation of 3x2 + 10xy + 3y2 =…

A: Axes are rotated through an angle 4π given equation is                             3x2+10xy+3y2=9…

Q: Write the equation 23x2 + 26√3xy - 3y2 - 144 = 0; θ = 30° in terms of a rotated x′y′-system using θ,…

A: Given Data The equation is 23x²+26√3 xy-3y²-144=0. The angle is θ=30°.   Put the value in…

Q: Write the equation 13x2 - 6√3xy + 7y2 - 16 = 0; θ = 60° in terms of a rotated x′y′-system using θ,…

A: Consider the given equation: Here the objective is to find the equation if the axis is rotated by…

Q: Write the equation x2 - 4xy + y2 - 3 = 0; θ = 45° in terms of a rotated x′y′-system using θ, the…

A: Given

Q: b) Find the counter-clockwise angle of rotation of axes to remove the xy term in the equation 12x² +…

A: Given.

Q: Eliminate the parameter t to find a Cartesian equation for: 3D² y = 3 + 5t The resulting equation…

A: Given that: x=t2…

Q: 3. Find five solutions to the equation x – 3 =;y and plot the solutions as points on a coordinate…

A: We will give 5 solutions to the given equation in a table. Here, x-3 = y/2 => y = 2x - 6. So,…

Q: Use the parametric equations shown below to answer the following. x = tV3 y = 3t - and

A: Given the parametric equations: (a) To plot the graph of these parametric equations using a…

Q: Express the equation in rectangular coordinates. (Use the variables x and y. ? = − 3pi/2

A:

Q: Find a parametric representation of the solution set of the linear equation.12x1 + 24x2 − 36x3 = 12

A:

Q: Convert the equation to rectangular form: r=2cscΘ cos2Θ=1

A: Consider the provided equations:

Q: Given parametric equations a = 2t and y = t² + 3, eliminate the parameter and write the resulting…

A:

Q: Write the parametric equations in rectangular form. y= 2f + 6 x = 5t – 8 -

A: Given,           The parametric equations are             y=2t2+6             x=5t-8

Q: Change 8x-2y^2= 2x^2 to polar form. Solve for r or some power of r.

A: The equation in the rectangular coordinates is given by 8x-2y2 = 2x2 To evaluate : The equation in…

Q: Convert r= 3 sec e to its equivalent Cartesian equation.

A:

Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the…

A:

Q: Write the equation with rectangular coordinates  r^2 = 7 cos 2theta

A:

Q: ASolve the equation 4x +20= 0 and write the resulting solution in the polar form, rZ0.

A:

Q: Find the coordinates of rotation of point () by an angle /2 a. -4 b. -4 с. 1 4. d. -1 4 77 7-

A:

Q: 5T Find the rectangular coordinates for the point (-1,).

A:

Q: Convert r = 3sin(θ) to an equation in rectangular coordinates.

A:

Q: In two or more complete sentences, explain how to find the time it takes for a rocket follow 3t and…

A: Introduction: A parametric equation is a type of equation that uses an independent variable called a…

Q: Write the equation 13x2 - 6√3xy + 7y2 - 16 = 0; θ= 60° in terms of a rotated x′y′-system using θ,…

A: Consider the given equation: 13x2 - 63xy + 7y2 -16=0 Here the objective is to find the equation if…

Q: Write the parametric equations in the given Cartesian form. X = x = 2t - t³, y = 9 - 2t

A: To convert the parametric equation to Cartesian equation.

Q: the Föllówing equation, identify the coordinates of the center an (x - 3)2 + (y + 2)? = 81

A: Comparing with standard form of equations of circle,

Q: Q1:- Find the Cartesian coordinates for the 3Tt 2:- (-1,- TC 1:-(2,-) 3:- (2,- 2.

A: Due to our guidelines I am solving only first three questions  Please repost other questions

Q: Write the following equation in the form y = mx + b. 1.2x+ 1.6y = 5.0, [-6,6] by [- 8,8] %3D The…

A:

Q: Eliminate the parameter t to find a Cartesian equation for: x = t^2 and y = 3 + 1t and express the…

A:

Q: Determine the new equation after rotated parallel to the principal axes for the equation below and…

A: Given The given equation is 2x2+4xy-y2=24. The general equation of two degrees is…

Q: when the axes are rotated through an angle x/4,find the transformed equation of 3x2+10xy+3y2=9

A:

Q: When the axes are rotated through an angle x/4,Find the transformed equation of 3x2+10xy+3y2=9

A:

Q: Write the standard equation of each círcle. Center (2, -8); r=-9 2 2 (x ) + ly Center (-9, -4); r=4…

A: let C(h,k) be the center of a circle and A(x,y) be a point on the circle .Therefore , the radius of…

Q: •x+yi dz Vaz + b and y = 5. Then, find the imaginary component of the result.

A:

Q: Replace the Cartesian equation (x+ 4)² + (y- 2)2 = 25 with equivalent polar eauation

A: Ans :   we will convert this given cartesian equation in polar equation  by putting - x = r cosθ…

Q: Convert the equation 5x2 + 2y? = 3z to spherical and cylindrical coordinates.

A: We have the following facts:

Q: Identify the equation without applying a rotation of axes. 2 10x² -8xy + y² +9x+3y-6=0

A: Given, 10x2-8xy+y2+9x+3y-6=0

Q: Eliminate the parameter and obtain the standard form of the rectangular equation.

A:

Q: b. Find a rectangular-coordinate equation by eliminating the parameter t.

A: