Write a polar equation in r and $ \theta $ of an ellipse with the focus at the origin,with the eccentricity and vertex at .

Question

Write a polar equation in r and $ \theta $ of an ellipse with the focus at the origin,with the eccentricity  and vertex at  .

Quizplus · Accepted Answer

The focus is at the origin, which means the distance from any point on the ellipse to the focus is equal to the distance from that point to the directrix. In polar coordinates, the distance from a point to the origin is r, so the distance from a point on the ellipse to the focus is |r - c|, where c is the distance from the origin to the directrix (which is the same as the distance from the origin to the vertex, since the vertex is halfway between the focus and directrix).

The eccentricity is given by e = c/a, where a is the distance from the origin to one of the endpoints of the major axis (which is also the distance from the origin to the vertex). So we have:

e = c/a
c = ea

We are told that the vertex is at (a,0), so the equation of the ellipse in polar coordinates is:

r = (ea)/(1 - e*cos(theta))

Plugging in the given values of e and a, we get:

r = (11ea)/(1 - 0.8*cos(theta))
r = 11eaae29_f48b_8e4b_87fe_c1256ec9b4de_TB2067_11 / (1 - 0.8*cos(theta))

Therefore, the answer is C.

Write a Polar Equation in R And θ \theta θ Of an Ellipse with the Focus at the Origin,with the Of an Ellipse

Write a Polar Equation in R And $\theta$ Of an Ellipse with the Focus at the Origin,with the Of an Ellipse