Question

A conic section is given by the equation 4x2 + 10xy + 4y2 = 36. Use...

A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.
Use rotation of coordinate axes through an appropriate acute angle θ to find the new equation of the conic section in the uv-coordinate axes , where x = u cos(θ) - v sin(θ) , y = u sin(θ) + v cos(θ). Then identify the conic section.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show that the equation represents a sphere, and find its center and radius.4x2+ 4y2+ 24x+ 4z2−20y=−57...
Show that the equation represents a sphere, and find its center and radius.4x2+ 4y2+ 24x+ 4z2−20y=−57 + 16z. Find a unit vector that has the same direction as the vector 3a−2b given that a= 2i+k and b=i−j+ 3k. Find a vector b with |b|= 5 such that the angle between the vector a=〈0,2〉and the vector b is π/3.(Hint: cos(π/3) =12).
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). y'' + 100y = 0; y1 = cos 10x I've gotten to the point all the way to where y2 = u y1, but my integral is wrong for some reason This was my answer y2= c1((sin(20x)+20x)cos10x)/40 + c2(cos(10x))
Find an appropriate integrating factor that will convert the given not exact differential equation cos ⁡...
Find an appropriate integrating factor that will convert the given not exact differential equation cos ⁡ x d x + ( 1 + 2 y ) sin ⁡ x d y = 0 into an exact one. Then solve the new exact differential equation.
6) (8 pts, 4 pts each) State the order of each ODE, then classify each of...
6) (8 pts, 4 pts each) State the order of each ODE, then classify each of them as linear/nonlinear, homogeneous/inhomogeneous, and autonomous/nonautonomous. A) Unforced Pendulum: θ′′ + γ θ′ + ω^2sin θ = 0 B) Simple RLC Circuit with a 9V Battery: Lq′′ + Rq′ +(1/c)q = 9 7) (8 pts) Find all critical points for the given DE, draw a phase line for the system, then state the stability of each critical point. Logistic Equation: y′ = ry(1 −...
1) State the main difference between an ODE and a PDE? 2) Name two of the...
1) State the main difference between an ODE and a PDE? 2) Name two of the three archetypal PDEs? 3) Write the equation used to compute the Wronskian for two differentiable functions, y1 and y2. 4) What can you conclude about two differentiable functions, y1 and y2, if their Wronskian is nonzero? 5) (2 pts) If two functions, y1 and y2, solve a 2nd order DE, what does the Principle of Superposition guarantee? 6) (8 pts, 4 pts each) State...
Your task will be to derive the equations describing the velocity and acceleration in a polar...
Your task will be to derive the equations describing the velocity and acceleration in a polar coordinate system and a rotating polar vector basis for an object in general 2D motion starting from a general position vector. Then use these expressions to simplify to the case of non-uniform circular motion, and finally uniform circular motion. Here's the time-dependent position vector in a Cartesian coordinate system with a Cartesian vector basis: ⃗r(t)=x (t) ̂ i+y(t) ̂ j where x(t) and y(t)...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary rivals? How will the acquisition of Reebok by Adidas impact the structure of the athletic shoe industry? Is this likely to be favorable or unfavorable for New Balance? 2- What issues does New Balance management need to address? 3-What recommendations would you make to New Balance Management? What does New Balance need to do to continue to be successful? Should management continue to invest...