Select the Graph That Represents the Given Conic Section $r = \frac { 13 } { 5 - 5 \sin \theta }$

question 5

Multiple Choice

Select the graph that represents the given conic section. If the conic is a parabola, specify (using rectangular coordinates) the vertex and directrix. If the conic is an ellipse, specify the center, the eccentricity, and the lengths of the major and minor axes. If the conic is a hyperbola, specify the center, the eccentricity, and the lengths of the transverse and conjugate axes. $r = \frac { 13 } { 5 - 5 \sin \theta }$

• A) Vertex: \(\left( 0 , \frac { 13 } { 10 } \right)\) Directrix: \(y = \frac { 13 } { 5 }\)
• B) Vertex: \(\left( - \frac { 13 } { 10 } , 0 \right)\) Directrix: \(x = - \frac { 13 } { 5 }\)
• C) Center: \(( 0,0 )\) Eccentricity: \(\frac { 5 } { 13 }\) Major axis length: \(\frac { 26 } { 5 }\) Minor axis length: \(\frac { 10 } { 13 }\)
• D) Vertex: \(\left( \frac { 13 } { 10 } , 0 \right)\) Directrix: \(x = \frac { 13 } { 5 }\)
• E) Vertex: \(\left( 0 , - \frac { 13 } { 10 } \right)\) Directrix: \(y = - \frac { 13 } { 5 }\)

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