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

Kyran Hudson

Kyran Hudson

Answered question

2021-02-12

Identify the conic section given by the polar equation r=41cosθ and also determine its directrix.

Answer & Explanation

smallq9

smallq9

Skilled2021-02-13Added 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
Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-26Added 2605 answers

Answer is given below (on video)

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