Write the equation of a conic that satisfies the conditions given. Assume the conic has one focus at the pole. ellipse, e = 0.5, directrix to focus: d = 10.

Question

Quizplus · Accepted Answer

For an ellipse with e = 0.5 and directrix to focus distance of 10, the equation of the conic in polar coordinates is given by:
r = ed/(1+e cos(theta))
Substituting e = 0.5 and d = 10, we get:
r = 5/(1+0.5 cos(theta))
Converting to rectangular coordinates, we get:
(x^2 + y^2)^(1/2) = 5/(1+0.5 cos(theta))
Squaring both sides and simplifying, we get:
4x^2 + 4y^2 + 9x^2 y^2 = 625
Therefore, the equation of the required conic is: 
4x^2 + 4y^2 + 9x^2 y^2 = 625, which corresponds to choice D.

Write the Equation of a Conic That Satisfies the Conditions