Question: Recall that Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 transforms to au2 + buv + ev2 + du +

Recall that Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 transforms to au2 + buv + ev2 + du + ev + f = 0 under a rotation of axes. Find formulas for a and c, and show that a + c = A + C.

Step by Step Solution

★★★★★

3.37 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

x u cos v sin y u sin v cos Ax 2 Au cos v sin 2 Au 2 cos 2 2uv cos sin v 2 sin 2 Bxy Bu cos v sin ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

955-M-C-D-E (2725).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

You saw in Lesson 9.7 that a transformation of the parent function f (x) = 1/x is a rotated hyperbola. Are there other kinds of rational functions that are also rotated hyperbolas? Recall that any...

Recall that the general quadratic equation is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Let A = 0, B = 4, C = 0, D = 0, E = 0, and F = - 1. a. Graph this equation. What type of conic section is formed? b....

Recall that [x] denotes the greatest integer less than or equal to x. Calculate each of the following integrals. You many use geometric reasoning and the fact that (a) (b) (c) (d) (e) (f) (g) (h) [x]...

The general form of the equation of a conic is given by which of the following? 10 4X3 + Boxy + Cy3 + Dx + Ey + F = 1 O AX 3 + Bxy + Cy3 + Dx + Ey + F= 0 O AX3 + Bxy + Cy3 + Dx2 + Ey2 + F = 1 O Ax2 +...

6. Let f(x, y) = ax? + bxy + cy? and g(x, y ) = f( x, y) = ax2 - bxy + cy". These forms represent precisely the same num- bers, but they are not necessarily equivalent (because the determi nant of...

The origin, (0, 0), is a fixed point for the system x' = x 7y 5xy 2 , y' = 2x 4y xy 2 (1) Show that no function of the form V = ax 2 + cy 2 can serve as a Lyapunov function for the system. (2) find a...

can you please do this in computer code not hand written? this is 7.2.1 in the mathematics and its history textbook 7.2.1 Show that a quadratic form ax2 + bxy + cy2 may be converted to a form ax2 +...

Find all local extrema of each of the following functions. a) f(x, y) = x2 - xy + y3 - y b) f(x, y) = sin x + cosy c) f(x, y, z) = ex+y cos z d) f (x, y) = ax2 + bxy + cy2, where a 0 and b2 - 4ac 0

All of the figures below are related mathematically because the equations used to describe each figure are similar. The general form of the equation for each is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0....

Linear independence and bases. Let V be the space of homogeneous quadratic polynomials in two variables, i.e. polynomials of the form fpx, yq " ax2 ` bxy ` cy2

Create an article review that addresses the following: what is the thesis (main idea) of the article? Why is (are) the author(s) writing about the topic? What facts are presented? How does it relate...

Investing: Inverse Mutual Funds Inverse mutual funds, sometimes referred to as "bear market" or "short" funds, seek to deliver the opposite of the performance of the index or category they track, and...

Generally, the accounting rate of return using the average investment will be Blank _ _ _ _ _ _ the internal rate of return. Multiple choice question. the same as lower than higher than

William Easterly in The White Mans Burden shares the following account by New York University Professor Leonard Wantchekon of how Professor Wantchekons village in Benin, Africa, managed the local...

A population following b(t) = 1.5t. For each equation for population size, find the following. a. The average rate of change between times 0 and 1.0. b. The average rate of change between times 0 and...

A population following b(t) = 2.0t. For each equation for population size, find the following. a. The average rate of change between times 0 and 1.0. b. The average rate of change between times 0 and...

A population following h(t) = 5.0t2. For each equation for population size, find the following. a. The average rate of change between times 0 and 1.0. b. The average rate of change between times 0...

A(n) eight-year bond has a yield of 9% and a duration of 7.204 years. If the bond's yield increases by 50 basis points, what is the percentage change in the bond's price? (Input the value as a...

Check My Work (2 remaining) eBook Given the graphs above, calculate the total fixed costs, variable costs per unit, and sales price for Firm A. Firm B's fixed costs are $120,000, its variable costs...

What is the beta? Is it larger than one or smaller than one? Why do you think it's larger or smaller than 1 ( hint: consider the industry ) ? I am choosing mIcrosoft corporatoon. The beta is 0 . 8 8...