Identify the conic section given by the polar equation displaystyle{r}=frac{4}{{{1}- cos{theta}}} and also determine its directrix.

Kyran Hudson 2021-02-12 Answered
Identify the conic section given by the polar equation r=41cosθ and also determine its directrix.
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Expert Answer

smallq9
Answered 2021-02-13 Author has 106 answers
Step 1
We convert the equation into rectangular form first
r=41cosθ
r(1cosθ)=4
rrcosθ=4
x2+y2x=4
x2+y2=x+4
x2+y2=(x+4)2
x2+y2=x2+8x+16
y2=8x+16
y2=8(x+2)
This is a parabola.
Step 2
Compare the equation with the standard form
(yk)2=4p(xh)
h=2,k=0
8p=2
or,p=2
Directrix =x=hporx=22orx=4
Answer: Parabola, x=4
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Jeffrey Jordon
Answered 2021-10-26 Author has 2064 answers

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