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disa [49]
3 years ago
11

Q6: Which is the graph of the polar equation r=1/1-sin theta.

Mathematics
1 answer:
AveGali [126]3 years ago
4 0

Answer:

The correct answer is C.

Step-by-step explanation:

The given equation is;

r=\frac{1}{1-\sin(\theta)}

This implies that;

r(1-\sin(\theta)=1

r-r\sin(\theta)=1

Let us write in Cartesian coordinates by substituting;

r=\sqrt{x^2+y^2} ,y=r\sin(\theta)

\sqrt{x^2+y^2}-y=1

\sqrt{x^2+y^2}=y+1

Square both sides;

(\sqrt{x^2+y^2})^2=(y+1)^2

This implies that;

x^2+y^2=y^2+2y+1

x^2=2y+1

y=\frac{1}{2}x^2-\frac{1}{2}

This is an equation of a parabola that opens upwards with a  y-intercept of -\frac{1}{2}.

The correct choice is C

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