What does r represent in the polar form equation?

Question

Hi
in the polar form equations r= (ep)/(1+esin(theta)) and etc, what does that "r" represent?
does it have to do with vertices or smth?
Thank you for your help!

Answer 1

r is the distance from the origin to the designated point. Theta is the angle that r makes with the x-axis. (r,theta) describe the location of a point in polar coordinates just as (x,y) do in cartesian coordinates.

You can convert between cartesian coordinates and polar coordinates by using r^2 = x^2+y^2, x=rcostheta, y = r sin theta, tan theta= y/x.

Answer 2

The curve runs to points at infinity in two directions, where sin θ = -2/3, so it must be a hyperbola. It has symmetry on θ = π/2, so that is one of the axes. There are solutions at rectangular coordinates (0, 1) and (0, 5). Those are the vertices, and the center is at (0, 3). That makes the radius 2. Imagine the right triangle formed by the y-axis, an asymptote, and a horizontal line through one of the vertices. The hypotenuse is the focus distance. The radius, 2, is the vertical leg, and we know that the direction of the hypotenuse (sin θ = -2/3). From that it follows that the focus distance is 3. If the focus distance, directrix distance, and radius are f, d, and r, then fd = r². d = r²/f = 4/3 So the directrices are horizontal and displace from the center by a distance of 4/3. The directrices: y = 5/3, y = 13/3 The foci: (0, 0), (0, 6) eccentricity = f/r = 3/2

Answer 3

generally r represent the radius of any curve which is the distance from the curve center or from the orgin to the curve surface r dosen't have to be constant as in in the circle
most cases r is varaiable and follow a certain equation to be solved at each piont u want to know r at like the equation u wrote in ur question

Answer 4

Distance from the center.

Answer 5

"r" stands for the distance from the point on the curve to the origin.