Q10: Determine the eccentricity, the type of conic, and the directrix for r = 11/6-5cos theta.

Accepted Solution

Answer:Eccentricity = 5/6 Type of conic section; EllipseDirectrix; x = -11/5Step-by-step explanation:The first step would be to write the polar equation of the conic section in standard form by multiplying the numerator and denominator by 1/6;[tex]r=\frac{\frac{11}{6} }{1-\frac{5}{6}cos theta }[/tex]The polar equation of the conic section is now in standard form;The eccentricity is given by the coefficient of cos theta in which case this would be the value 5/6. Therefore, the eccentricity of this conic section is 5/6.The eccentricity is clearly between 0 and 1, implying that the conic section is an Ellipse.Since the conic section is in standard form, the numerator is the product of eccentricity and the value of the directrix, that is;e*d = 11/65/6*d = 11/6d = 11/5Since the denominator has a minus sign then the ellipse opens towards the right and thus the equation of its directrix is;x = -11/5