Question

Write a polar equation of an ellipse with its focus at the origin and satisfies the given conditions: eccentricity 6/7, directrix x = 7.

Answer 1

The polar equation of an ellipse with its focus at the origin and a directrix given by x = 7 is r = (ed)/(1-e*cos(theta)), where e is the eccentricity and d is the distance to the directrix.

Step-by-step explanation:

The polar equation of an ellipse with its focus at the origin and a directrix given by the equation x = 7 can be written as:

r = \frac{{ed}}{{1-e\cos(\theta)}}

where e is the eccentricity of the ellipse and d is the distance from the origin to the directrix. In this case, the eccentricity is given as 6/7, so e = \frac{6}{7}, and the distance from the origin to the directrix is 7, so d = 7.

Substituting these values into the equation, we get:

r = \frac{{\left(\frac{6}{7}\right)\cdot 7}}{{1-\left(\frac{6}{7}\right)\cdot\cos(\theta)}}