Question

convert the equation to polar form
x^2-y^2=7

Answer 1

(use variables r and theta as needed)

Answer 2

@jim_thompson5910 :)

Answer 3

substitute x=rcosθ and y=rsinθ

Answer 4

and that would be the final answer?

Answer 5

\[(rcos \theta)^2- (rsin \theta)^2=7\]

Answer 6

@alekos

Answer 7

No, I would go further

\[r^{2}(\cos ^{2}\theta-\sin ^{2}\theta)=7\]

Answer 8

and the trig identity can now be simplified

Answer 9

\[r^2(\cos^2 \theta) = 7\]

Answer 10

no way. what is cos2θ ?

Answer 11

haha oops sorry I means cos2theta

Answer 12

\[r^2(\cos2 \theta) = 7\]

Answer 13

very good and now we can go further
\[r ^{2}=7\sec2\theta \]

Answer 14

hmm I just need to write it in polar form. Should we be going this far?

Answer 15

did you mean cos?

Answer 16

oo I see what you did, okay, nevermind.

Answer 17

we are heading to the final polar form

Answer 18

just take the square root of both sides and you have the final polar form

Answer 19

\[r=\sqrt{7\sec2 \theta}\]

Answer 20

beautiful. thats it!

Answer 21

yay! thank you :)

Answer 22

hrmm they don't like that answer -.-

Answer 23

@Miracrown

Answer 24

oh, I figured it out :)
they wanted
r^2(cos2theta)=7