## Convert the equation r cosine theta equals 9 sine (2 theta )to Cartesian coordinates. Describe the resulting curves. Choose the correct equa

Question

Convert the equation r cosine theta equals 9 sine (2 theta )to Cartesian coordinates. Describe the resulting curves. Choose the correct equations below. A. (x minus 9 )squared plus y squared equals 9 squared and x equals 0 B. x squared plus y squared equals 9 squared and x equals 0 C. x squared plus (y minus 9 )squared equals 9 squared and x equals 0 Your answer is correct.D. (x minus 9 )squared plus (y minus 9 )squared equals 9 squared and x equals 0 Choose the best description of the curves described by this equation. A. a circle centered at (negative 9 comma 0 )with a radius of 9 and the y dash axis B. a circle centered at (0 comma 9 )with a radius of 9 and the y dash axis Your answer is correct.C. a circle centered at (0 comma negative 9 )with a radius of 9 and the y dash axis D. a circle centered at (9 comma 0 )with a radius of 9 and the y dash axis

in progress 0
17 hours 2021-09-15T20:55:47+00:00 1 Answer 0

The curve is a circle of radius 9 centered at the point (0,9) and the equation is

Step-by-step explanation:

Proceed as follows:

Take . Then

Multiply both side by . Then

Use the following substitution . Then

By cancelling out x on both sides we get the following equation

or

Recall that given a expression of the form we can complete the square by adding an substracting the amount . So, we get . In our case, we will complete the square for y, then

. Then

or

.

Recall that the equation of a circle is given by where (h,k) is the center of the circle and r is the radius. In our case we have h=0, k = 9 and r = 9. So it is a circle of radius 9 centered at the point (0,9)