Find the values of e, a, b, and c.
-$$r = \frac { 21 } { 5 - 2 \cos \theta }$$
A) $\mathrm { e } = \frac { 2 } { 5 } , \mathrm { a } = 5 , \mathrm {~b} = \sqrt { 21 } , \mathrm { c } = 2$
B) $\mathrm { e } = \frac { 2 } { 5 } , \mathrm { a } = 21 , \mathrm {~b} = 4 , \mathrm { c } = 5$
C) $\mathrm { e } = \frac { 5 } { 2 } , \mathrm { a } = 2 , \mathrm {~b} = \sqrt { 21 } , \mathrm { c } = 5$
D) $e = \frac { 5 } { 2 } , a = 21 , b = 4 , c = 5$

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the form of an ellipse's polar equation, $r = \frac{ep}{1 - e\cos\theta}$, where $e$ is the eccentricity, $p$ is the semi-latus rectum, and $a$, $b$, and $c$ are the ellipse's semi-major axis, semi-minor axis, and focal length, respectively. Comparing the given equation to the standard form, $e = \frac{2}{5}$, $p = 21$, and since $p = \frac{b^2}{a}$, we can find $a$, $b$, and $c$ with $c^2 = a^2 - b^2$ and $e = \frac{c}{a}$.

Find the Values of E, A, B, and C r=215−2cos⁡θr = \frac { 21 } { 5 - 2 \cos \theta }r=5−2cosθ21​

Find the Values of E, A, B, and C $r = \frac { 21 } { 5 - 2 \cos \theta }$