ANSWER:
r = [tex] \frac{1}{cos2(theta)} [/tex]
Explaination:
Convert the given curve into the the polar form.
x = rcosθ
y = rsinθ
in f(x,y) = (x²-y²) - √(x²+y²) = 0
put the values of x & y in given curve equation.
We get at,
g(r,θ) = (r²cos²θ - r²sin²θ) - √(r²cos²θ + r²sin²θ) = 0
g(r,θ) = r²(cos²θ - sin²θ) - √r² = 0
We know that,
cos²θ - sin²θ = cos2θ
g(r,θ) = r²(cos2θ) - r = 0
Solve for r
Finally we get:
r = [tex] \frac{1}{cos2(theta)} [/tex]
