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Nimfa-mama [501]
3 years ago
12

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

Mathematics
1 answer:
masya89 [10]3 years ago
8 0
ANSWER

b.

EXPLANATION

The given polar equation is,

r = \frac{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.

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