Question

(Q7) Determine the graph of the polar equation r = 12/6+4 cos theta.

Answer 1

Answer: B

Step-by-step explanation: edge

Answer 2

ANSWER

b.

Step-by-step explanation

The given polar equation is,


`r = (12)/(6 + 4 \cos( \theta) )`

Cross multiply to get,


`r(6 + 4 \cos( \theta) ) = 12`


`6r + 4r\cos( \theta) ) = 12`

Substitute,


`r\cos( \theta) = x`

and


`r = \sqrt{ {x}^(2) + {y}^(2) }`


`6 \sqrt{ {x}^(2) + {y}^(2) } + 4x = 12`


`3\sqrt{ {x}^(2) + {y}^(2) } + 2x = 6`


`3\sqrt{ {x}^(2) + {y}^(2) } = 4 - 2x`


`9({x}^(2) + {y}^(2)) =( 4 - 2x ) ^(2)`


`9{x}^(2) + 9 {y}^(2) =16 - 16x + 4x ^(2)`


`5{x}^(2) + 9 {y}^(2) + 16x = 16`

This is an ellipse whose center is shifted to the left with orientation on the x-axis

The correct choice is B.