Question

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

Answer 1

c on edge

Explanation:

Answer 2

The correct answer is C.

Explanation:

The given equation is;

`r=(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=√(x^2+y^2) ,y=r\sin(\theta)`

`√(x^2+y^2)-y=1`

`√(x^2+y^2)=y+1`

Square both sides;

`(√(x^2+y^2))^2=(y+1)^2`

This implies that;

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

`x^2=2y+1`

`y=(1)/(2)x^2-(1)/(2)`

This is an equation of a parabola that opens upwards with a y-intercept of
`-(1)/(2)`.

The correct choice is C