Question: Let F and F' be fixed points with polar coordinates (a, 0) and (-a, 0), respectively. Show that the set of points P satisfying |PF|

Let F and F' be fixed points with polar coordinates (a, 0) and (-a, 0), respectively. Show that the set of points P satisfying |PF| |PF'| = a2 is a lemniscate by finding its polar equation.

Step by Step Solution

★★★★★

3.45 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

r 4 2a 2 r 2 a 4 4a 2 r 2 cos2 a 4 r 4 4a ... 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 (2777).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Find the distance between the points with polar coordinates (1, /6) and (3, 3/4).

Find a formula for the distance between the points with polar coordinates (1, 1) and (2, 2)

Find the distance between the points with polar coordinates 4, 4/3d and 6, 5/3d.

How do I solve this? 1. 1) a) (Ex. 3.1.12 (b), 3pts) Show that T(x, y, t) = e-kt (cos(x) + cos(y) ) satisfies the two dimensional heat equation OT k + = ay2 at b) (Ex. 3.1.29 (a), 3pts) Let f, g be...

3. Show that C is a hyperbola if e > 1. 4. Show that the polar equation ed 1 + e cos 0 represents an ellipse if e 1. 5. For each of the following conics, find the eccentricity and directrix. Then...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

854 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES 9. 20. Jessica and I at 2 oh ; h (x , y ) = -, x = 1/2, y = 1712 paths that make a with velocity va 10. "J : f ( x , y , Z ) = xy - 22, x = rcos0,...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Using the Internet or the Strayer databases, select a different company of your choice but this time analyze the Statement of Cash Flows for that chosen company. Next, discuss the change in cash...

Under the set-up of Theorem 8.30, explain why j max V.VI = . . .

5. For every item in the inventory managers must decide: (a) The source from which it can be bought at the cheapest rate. (b) How much to buy and when to place orders. (c) The cost of placing an...

In 2012, an unexpected and persistent drought affected crop production across Europe, including the United Kingdom. The most widely grown crop in the United Kingdom is wheat. Use a demand and supply...

The following discrete-time dynamical systems have slope of exactly -1 at the equilibrium. Check this, and then iterate the function for a few steps starting from near the equilibrium to see whether...

The logistic dynamical system with r = 2.

The dynamical system xt + 1 = xt e1-xt.

What is the present worth of all disbursements and receipts during the life time of the project, evaluated at the beginning of the first year, if the project has the following costs: Phase 1 labor...

Can someone explain this question with working for me please. 4. Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of...

Suppose that you can got a 30-year mortgage at 8% interest. How much can you afford to borrow if you can afford to make a monthly payment of $1,000